Agent-based Computational Economics: Exploring the Evolution of Trade Networks

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Agent-based Computational
Economics: Exploring the
Evolution of Trade Networks
Gemma Hagen
〈gh206@doc.ic.ac.uk〉
Department of Computing
Imperial College London
Supervisor: Abbas Edalat 〈ae@doc.ic.ac.uk〉
Second Marker: Francesca Toni 〈ft@doc.ic.ac.uk〉
June 26, 2009

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Abstract
As the field of economics seeks to further its understanding of the links between
the micro and macro sides of the area, economists are becoming increasingly
appreciative of agent-based models. Cross-silos approaches to problems are pro-
viding for a new way of thinking about how to explain complex phenomenon in
science. Agent-based modelling provides a novel and effective way of explaining
how such complex systems arrive at macro phenomenon through attempting to
grow said societies. The project that I am undertaking is an extension of the
work completed by Allen Wilhite which is documented in his paper “Bilateral
Trade and Small-world Networks.” His aim was to explore the efficiency of var-
ious trade network formations through an agent based simulation. In his work
agents are able to produce or trade one of two goods. The report documents
the extensions to this model in order to explore the evolution of trade networks
and traits of agent behaviour. Furthermore, dependencies between agents are
examined as well as wealth distributions. The extensions are evaluated both in
the context of the simulation and the real world.

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Acknowledgements
It is with great pleasure that I acknowledge the help, guidance and support
of my supervisor, Prof. Abbas Edalat. Without his critical assessment of my
methods, and willingness to provide both support and suggestions for solutions
to problems faced, I would not have been able to achieve the results displayed
here. I especially appreciate the brainstorming sessions which furthered my
insight into the complexities of human interaction, and significantly shaped the
direction of my project.
I would also like to thank Dr. Francesca Toni, my second marker for re-
viewing the progress of my project and giving me pointers to current research
and platforms for implementation of agent-based simulations. In addition, her
challenging questions permitted me to develop a greater understanding of the
model at hand.
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Contents
1 Introduction
5
1.1 Key Contributions . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2 Background
8
2.1 Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.1.1 Economic History: An Extremely Brief Overview . . . . .
8
2.1.2 Economics as a Complex Adaptive System . . . . . . . . 10
2.2 Complex Adaptive Systems . . . . . . . . . . . . . . . . . . . . . 13
2.3 Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Agent Based Modelling . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Inspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Model
22
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Initial Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 With whom can an agent trade? . . . . . . . . . . . . . . 25
3.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1 Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.2 Specialisation . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.3 Wealth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Increasing Trade
43
4.1 The Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.1 Inspecting Agent Behaviour . . . . . . . . . . . . . . . . . 45
4.2.2 Global Trends . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 Introducing Consumption For Survival
55
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
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5.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.1 Evaluating values for constants . . . . . . . . . . . . . . . 57
5.3.2 Bankruptcy Chains . . . . . . . . . . . . . . . . . . . . . . 64
5.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6 Permitting Agents to Remember Encounters
74
6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.3.1 Loyalty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.3.2 Pure Traders . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3.3 Specialisation . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7 Learning: Trade of Knowledge
88
7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.1.1 The Importance of Structure . . . . . . . . . . . . . . . . 89
7.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.2.1 Decision to Learn . . . . . . . . . . . . . . . . . . . . . . . 91
7.2.2 Deciding who to learn from and who should be exchanged 92
7.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.3.1 Specialisation, wealth and price dispersion . . . . . . . . . 95
7.3.2 Emerging Globalisation . . . . . . . . . . . . . . . . . . . 99
7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8 Evolution as a method of gaining insight
107
8.1 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 107
8.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8.2.1 Fitness Scores . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.2.2 Agents to make up the new population . . . . . . . . . . . 109
8.2.3 Generating offspring: Crossover and Mutation . . . . . . 111
8.3 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9 Implementation
117
9.1 An Alternative Design Choice . . . . . . . . . . . . . . . . . . . . 117
9.1.1 JADE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.2 The simulation: Java & Python . . . . . . . . . . . . . . . . . . . 118
9.2.1 Java . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9.2.2 Python . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.2.3 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . 120
9.3 PDF Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
9.4 Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
9.5 How it works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
9.6 Distributing Simulations . . . . . . . . . . . . . . . . . . . . . . . 130
9.7 Software Development Process & Testing . . . . . . . . . . . . . 132
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10 Conclusion and Further Work
133
10.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
10.2 Alterations to the Model . . . . . . . . . . . . . . . . . . . . . . . 136
10.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.4 Concluding Thoughts . . . . . . . . . . . . . . . . . . . . . . . . 137
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Chapter 1
Introduction
This report documents an investigation into the applicability and credibility
of agent-based modelling to the study of economics. A simulation engine is
created, using a fast and fairly rigid Java core, supplemented by an easily ex-
tensible scripting layer, with a simple web interface allowing customisation of
operational parameters and easy deployment of simulations across multiple ma-
chines. Basing the core model on the work by Allen Wilhite, a world in which
agents are able to produce and trade one of two goods is developed. Various net-
work topologies restrict with whom agents can trade and, in addition, through
whom agents can search in order to find a trade partner. Extensions are added
to give agents the opportunity to learn about suitable trade partners through
remembering exchanges, and a further type of exchange is permitted - the ex-
change of the knowledge of the existence of agents in order to grow a global
economy from the bottom up. This can be considered to be analogous to a sim-
plified model of human communication in business. In addition, investigations
into the effect of necessary consumption are added to enhance the realism of the
model and permit the analysis of bankruptcy of agents. This enforces agents
to consume goods, encapsulating the finite nature of the resources, for instance
fuel, upon which all businesses in the real world depend. Finally, a genetic al-
gorithm is employed in order to gain insight into what makes a wealthy agent,
which highlights both the successes and limitations of the model adopted.
As extensions are added, the effect on the dynamics and the evolution of
the simulation is thoroughly evaluated, both in the context of how the model is
improved, and with respect to how well findings fit with economic theory.
Economics is currently receiving criticism, especially given the current reces-
sion, from both academics outside the field and economists themselves. As the
world becomes more globalised more interdependencies arise, leading to com-
plexity that the models and assumptions of Neoclassical economics are strug-
gling to address. Economics as it is today is becoming increasingly outdated.
There exists a need for change. As cross-silos approaches to complex problems
gain pace in the academic world, and research into complex systems is furthered,
it becomes increasingly apparent that the economy is not as simple as it once
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was. It is necessary to revitalise economics, bringing it up to speed through
adopting perspectives from complex systems, and studying it as such. This en-
tails embracing the notion of emergence, which describes the process by which
macro phenomena emerge from micro interactions. In addition, focus lies not
on the elements composing the system, but rather on the interactions between
these elements. Agent-based modelling seems like a powerful tool to facilitate
developing models and growing societies, allowing examination of how micro
interactions can result in these macro phenomena.
This report is illustrative of the fact that agent-based modelling has the
potential to provide huge insight and compelling results, facilitating the expla-
nation of the dynamics of the billions of people interacting to form the economy.
In addition, by requiring that agents do nothing but strive to further their po-
sition in the economy by maximising their utility, many complex phenomena in
economics are witnessed. Agents begin to specialise in whether they produce or
trade, and traders become loyal to their partners. Wealth distributions are anal-
ysed and, as the model is developed, become increasingly realistic. That the rich
get richer and the poor get poorer is shown not to be solely a saying, as wealth
condenses on to the already wealthy. Learning facilitates the trade of knowledge
of agents, and in a world of free trade without barriers, globalisation emerges
and demonstrates its efficiency as prices converge, and creative destruction is
witnessed as the most effective agents rise to become bridges across districts.
In addition, the architecture of this globalisation is examined and compared to
that of the real world.
1.1 Key Contributions
• The implementation of an extensible economic simulation, leveraging mod-
ern scripting language paradigms which facilitate rapid and simple de-
velopment of complex logic describing the way in which agents interact.
(Section 9.2)
• A simple web interface, enabling fast addition of configuration options,
permitting easily customisable simulations.(See Section 9.4)
• The evaluation of results attained from the simulation, in both an eco-
nomic context and in the context of the performance of the model. (See
Sections 3.3, 4.2, 5.3, 6.3, 7.3, 8.3)
• A critical analysis of potential limitations of the model adopted. (See
Section 10.1)
• Through results obtained, suggestions of the importance of network struc-
ture in the economy, as well as suggestions for direct applicability of these
ideas are made. (See Chapters 4, 5)
The report consists of a description of Wilhite’s model and a description of
the motivation for and implementation of extensions, followed by a thorough
evaluation for each. Table 1.1 summarises the motivation for extensions.
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Extension
Motivation
Restriction of the percentage of
agents who can produce both
goods.
Wilhite’s model inadvertently prohibited large amounts of trade,
and a larger volume of trade was necessary to soundly evaluate
the formation of trade networks.
Forcing agents to consume one of
the goods.
Intended to capture the fact that business in the real world incur a
need for resources to facilitate production (for instance factories)
and trade (for instance shipping costs), and to analyse dependency
in networks through investigating “bankruptcy chains”.
Permitting agents to remember
exchange.
Intended to investigate the usefulness of memory to agents, specif-
ically traders, and to better reflect the common occurrence in re-
ality of returning to the same source to buy or sell through having
learned that it is least costly / most profitable.
Adding exchange of the knowl-
edge of the existence of other
agents.
Intended to attempt to grow a global economy, and to overcome
the limitation in Wilhite’s model that agents acting as “bridges”
for trade between districts were chosen at random.
Addition of a genetic algorithm
to evolve agents
Intended to gain insight into what makes a wealthy agent, given
the initial conditions of the simulation.
Table 1.1: Summary of extension with corresponding motivation
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Chapter 2
Background
2.1 Economics
Neoclassical economics is the dominating force of economics today. It steers
the decisions of governments in making economic policies, and of companies in
mergers and acquisitions. It commands text books of A-Level and undergradu-
ate studies and its influence has been hugely beneficial for over a hundred years.
All of the G8 countries have avidly followed the theories and solutions it has
introduced, and are obviously extremely wealthy from doing so. However, over
the past decade, there has been increasing criticism over the robustness of these
theories. People’s concern over the correlation of these theories to the real world
is growing and companies with high stature, such as General Electric, have even
closed down their economic departments. This is not to say that the theories
are useless, moreover, there exists a progressive consensus that the field is not
fulfilling its potential as a science - that economics is in need of a makeover.
This is not just a wave of concern coming from scientists outside the field, but
economists themselves are engaging in self critical analysis of the area. Joseph
Stiglitz was quoted in an article in The New Yorker by Cassidy [5] “Anybody
looking at these models would say they can’t provide an accurate description of
the real world.”
2.1.1 Economic History: An Extremely Brief Overview
Obviously an account of economic history is hardly feasible, however, it is in-
teresting to see the development of the field - or at least the key turning points.
A good place to start would be with the revelations of Adam Smith. Adam
Smith was a moral philosopher turned economist who brought huge ideas to, at
the time, the underdeveloped field. Smith attempted to answer two important
questions, namely how wealth is created and how it is allocated. For the first
question, he argued that labour productivity, which was largely dependent on
the division and specialisation of labour, is what creates wealth. It is the act of
using raw materials to create items that other people want in an efficient man-
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ner. For the latter, he claimed that if people were free to trade on their own, the
pursuit of an individual’s self interest would drive them to provide the resources
people want at the price they are willing to pay.[17] This came to be known as
the invisible hand and is a good example of emergent behaviour since through
an individual’s pursuit of self interest they would be inadvertently benefiting
society as a whole, a macro phenomenon, through efficient resource allocation.
Smith explained that the key mechanism in these competitive markets was the
price at which people trade. This lead to the idea that the market clears at the
point where supply is equal to demand - a core concept in neoclassical economics
today.
Although this was a profound idea, economics still massively lacked mathe-
matical rigour. It was Walras, along with his compatriots, who strived to find a
way of bringing this element to the table. His conjecture was that the equilibria
witnessed so frequently in nature was analogous to that of markets clearing.[27]
The notion of equilibrium however is more complex than simply opposing forces
coming in to balance as there are many sorts of equilibrium apparent in different
systems. For instance, dynamic systems, such as the Earth orbiting the Sun,
are subject to a dynamic equilibrium. However, knowing if this was a stable
or unstable equilibrium was extremely difficult given the mathematical tools of
the time. There are also systems with multiple equilibrium points, however this
leads to the difficulty and sometimes impossibility of determining exactly which
equilibrium a system will fall in to. Walras therefore decided that for every
commodity there is exactly only one equilibrium point, and that this point is
the price at which people are willing to trade at. He went on to develop a model,
known today as a Walrasian model.
In this model, individuals are endowed with an amount of every possible
good, and an individual’s preference, or utility, towards goods is heterogeneous.
The idea is that if people want to trade, the system is out of equilibrium and
therefore a more optimal allocation of goods exists. If you could establish prices
to trade at, people could trade to move to a more satisfied state. Once everyone
was as satisfied as possible, no one else would want to trade and hence equilib-
rium is reached. Prices would be set by an auctioneer using one of the goods
as money. As in a usual auction house, if there was more demand than supply,
prices would increase and vice versa. This would be done across all goods, and
once the price of every good was established, then and only then could people
trade. His model assumed that people would act rationally and in their own self
interest. Additionally, and importantly, the existence of the auctioneer, makes
it mathematically simpler but also a centralised (thus unrealistic) system.[18]
Pareto was also hugely influential. He deduced that people would not make
trades that would make them worse off, and hence every trade makes society as a
whole better off. Today this is called Pareto Superior trading, and means people
will only engage in trades that are good for both of them, which is what the
model of trade employs in this report. With this, the market would eventually
reach an equilibrium which is Pareto Optimal, where no individual can trade
without making someone worse off, in other words, there are no more Pareto
Superior trades to be made.[27, 1]
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Both Pareto’s and Walras’ ideas were extremely successful, although Walras’
model assumed certainty, or perfect information. It was Arrow and Debreu[27]
who tied the theories of Walras and Pareto together, resulting in the Neoclassical
General Theory of Equilibrium. They conjectured that markets will coordinate
themselves and reach Pareto Optimal prices, however, this would be so regard-
less of uncertainty.
Now the basics of neoclassical economic theory have been laid down, we are
in a better position to understand the fundamental limitations of this approach.
One of the difficulties of economics as we know it in text books, is that it is
very much focussed on macro results, and lacks the ability to understand the
necessary micro interactions that can result in these macro trends. It is fair
to say that this top down approach of analysis adopted by economics works
very well for many fields, However, it is also the case that many of the biggest
problems in nature are complex systems. These sort of systems benefit far more
from a bottoms up approach. The Santa Fe Institute, in New Mexico, USA, does
huge research in to complex systems. They are also extremely pro cross silos
approaches to problems. They recognise and value the fact that many problems
are better understood through utilising knowledge from many different areas of
expertise. Economics and the Santa Fe Institute crossed paths in 1987 when
Citicorp agreed to fund cross silos research into the field.[19] It was time to
accept that economics may not be fulfilling its potential as a science, and was
also time to utilise the expertise of leading researchers in various fields.
2.1.2 Economics as a Complex Adaptive System
At the Santa Fe Institute, days of discussion amongst economists, physicists,
biologists, mathematicians and computer scientists regarding the current ap-
proach of economics lead to some interesting conclusions. It was realised that
economics was fairly “behind the times” when it came to the mathematics it
was based on. However, the scientists were somewhat impressed that economists
had managed to bend the tools at their disposal so well creating such impressive
results for such a long period of time.
A fundamental obstacle that the scientists and mathematicians saw was
the assumptions in economic theory. It is true to say that assumptions are
both apparent and useful across all disciplines however they must be correctly
formed. Assumptions must reflect a simplified reality, they must not be a direct
contradiction or an unattainable state. These concerns did exist in the days of
Walras, however the progression Neoclassical theory continued with economists
largely ignoring these concerns. At this time, people argued that so long as the
output of the equations was realistic then the assumptions it was grounded on
are of arbitrary concern. However, later on, people began to take a different
turn. Herbert Simon from Carnegie Mellon University pointed out that the point
of science was to explain, not predict. It does not suffice to validate a theory
through verifying the end point or conclusion is as expected, it is necessary to
validate the entirety of the theory - including the assumptions. [27, 19]
Probably the most debated assumption of economic theory is the model
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used for human behaviour. This is manifested in the assumption of perfect
rationality which makes unattainable and unrealistic assumptions about both
the world we live in and the way in which we engage with our environment. For
instance, it assumes that we will always act in our own economic self interest,
and that in making basic everyday decisions we do so with perfect information.
For instance, when I make a decision to make a purchase of some arbitrary
good, I have taken into account every other possible thing this could be spent
on, assure myself that the increase in utility gained from purchasing this good
is that which maximises my utility. I am certain that this specific Tesco offers
the best price; not to mention accounting for whether or not this money should
be put in to a savings account instead, which assumes knowledge of current and
estimated future interest rates, government expenditure and so on. This decision
making process evidently would result in a monstrosity of calculations on my
part, involving information that is difficult to get, if possible at all. The truth
however, is that this does not correctly reflect a model of human behaviour.
In reality, we are not good at difficult calculations over split seconds. Our
intelligence is in the ability to make such quick decisions with ambiguous and
incomplete information on a regular basis. People also have the ability to learn
and apply knowledge to new situations through pattern recognition - a very
different picture than that of neoclassical theory. This perfect information is an
example of something that will be explored in the model implemented - partly
to see if it’s necessary to have perfect information to reach an equilibrium, and
partly to compare what happens with and without it; perhaps leading to gaining
an insight into which offers a better reflection of reality.
In addition, the world we live in is often not simplified by neoclassical theory
but altered. For instance, the existence of an auctioneer is something that (with
the exception of an auction house!) never happens. It is not the case that the
supermarket is centralised - they don’t have to hold auctions for us to buy our
weekly shopping. On the contrary, our networks are very much decentralised,
and as such my model will veer from the Walrasian model by removing the
auctioneer.
Another issue is that of the representation of time in neoclassical theory.
In reality trawling for information, making trades and learning all take time
whereas it’s usually instantaneous in neoclassical theory. The importance of
this is that to properly understand systems behaviour it is necessary to have an
idea about the sort of time scales you are looking at.
A Step in the Wrong Direction
Again it is important to clarify that the neoclassical economic model is not
entirely crazy. It is not true that the model of supply and demand moving to
form an equilibrium is misclassified, it is a fair estimate, but rarely happens. It is
also true that prices do sometimes converge, and markets can act as if they are in
a form of equilibrium. However, the fact that these models aren’t as bullet proof
as something like “speed equals distance over time” leads us to some interesting
questions. Namely, why is it the case that these models aren’t often realised?
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Is it really because of “exogenous shocks” to the economy constantly moving
it out of equilibrium? Or are these “exogenous” factors actually “endogenous”
to the system itself? Is the scope of the economic system wider and far more
complex than originally anticipated?
In an attempt to answer these question it was necessary to discover exactly
where these models came from. The physics that was borrowed by Walras
and his compatriots to bring mathematics and economics together was from
classical thermodynamics. However, at this point in time only the first law of
thermodynamics was in existence.[27]
Thermodynamics studies the behaviour of energy flow in natural systems.
From the study of this area, some fundamental laws have been observed in
our universe. The first law of thermodynamics otherwise known as the Law of
Conservation of Energy, says:
The change in a system’s internal energy is equal to the difference
between heat added to the system from its surroundings and work
done by the system on its surroundings.
All this means is that heat added to the system can only do two things
- change the internal energy of the system or cause the system to do work.
Mathematically this law is:
U
2
− U
1
= δU = Q − W
Q = δU + W
where U
1
is the initial internal energy, U
2
the final internal energy, Q is the
heat transferred into (or out of) the system, W is the work performed by the
system or on the system and δU is the change in energy.[20]
A consequence of this law is that if the energy of a system is conserved, the
system is guaranteed to reach an equilibrium. The only thing that can move it
from this equilibrium is adding energy from outside the system - exogenously. It
states that the total energy of the system and its surroundings remains constant.
Trivially this relates to the theory of supply and demand - prices will reach
equilibrium through the tensions between supply and demand unless an outside
force shifts it from this equilibrium. It also implies, that if the economy follows
this law, wealth can not be created - the economy must begin with a finite set
of resources that create a finite set of goods.
However, this leads to some debate, especially when you do look at the
second law of thermodynamics. The second law of thermodynamics deals with
not how to do something but instead constrains what can be done:
It is impossible for a process to have as its sole result the transfer
of heat from a cooler body to a hotter one.
It says we are restricted by nature to achieve certain kinds of outcome with-
out putting a lot of work into it. Hence it is closely tied to the conservation of
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energy, just as the first law is. This law also has a lot of applications outside of
physics since it is closely tied in to the notion of entropy. In terms of entropy,
the second law reads:
In any closed system, the entropy of the system will either remain
constant or increase.
This means a system that goes through a thermodynamic process can never
be returned to the exact same state it was in before, a definition used for the
arrow of time as entropy of the universe will always increase over time according
to the second law. Entropy is a measure of disorder, and hence the universe’s
disorder is always increasing and work has to be done in order to bring order to
the system; the system decays into disorder and eventually comes to rest.[20]
These two laws lead us to a distinction between open and closed systems. A
closed system is one which can exchange heat and work, but not matter with its
surroundings. In contrast, an open system is a system where matter can also be
added or removed from it, hence open systems interact with their environment.
The question now is what does this all have to do with the economy? The econ-
omy is made up of energy, matter and information and hence is not an abstract
notion - it exists physically and thus is exposed to the laws of physics. Energy
enters the economy, we fight entropy as we fight to create order, and export
disorder, hence obeying the second law through throwing out waste such as pol-
lution and greenhouse gases. Thus economies are literally open systems. Since
the neoclassical model is so heavily tied to the First Law of Thermodynamics,
perhaps this is what has restricted the potential of economics. The conjecture
however that the economy is in fact a complex adaptive system necessitates
defining exactly what this means, which is the topic of the next section.
2.2 Complex Adaptive Systems
In Eric Beinhocker’s book he argues that the economy is in fact a complex
adaptive system and thus should be studied as such. In this section I will
briefly describe what these systems are and attempt to explain how this relates
to the economy.
Complex Adaptive Systems are a special case of Complex Systems, so we
will begin by looking at what a complex system is. Complex systems are only
recently becoming better understood, however the notion of complex systems
has existed for over 100 years. In 1887, Oscar II, who was the King of Norway
and Sweden, offered a prize for anyone who could tell him whether the solar
system was stable. It was Poincare who showed that it was impossible to find a
solution to the trajectory of just three planets interacting in a non-linear fashion.
Fortunately he won the prize and this problem is known today as the 3 Body
Problem.[6] His findings were put aside for many years, and it is only relatively
recently with the introduction of computerised simulations that people realised
he had predicted chaotic motions and complex systems.
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The definition of a complex system comes in many forms, here are just but
a few.[6]
...you generally find that the basic components and the basic laws
are quite simple; the complexity arises because you have a great
many of these simple components interacting simultaneously. The
complexity is actually in the organization the myriad possible ways
that the components of the system can interact. (Stephen Wolfram,
quoted in Waldrop, 1993)
...to understand the behaviour of a complex system, we must un-
derstand not only the behaviour of the parts but how they act together
to form the whole. (Bar-Yam, 1997)
A complex system is a system for which it is difficult, if not im-
possible to restrict its description to a limited number of parameters
or characterising variables without losing its essential global func-
tional properties. (Pavard, 2000)
Hence a complex adaptive system is a complex system with the added ca-
pability of learning and changing over time. Complex systems in general have
many properties, such as emergence, short range non linear relationships, non-
determinism, limited functional decomposability and distributed character of
information. It is also important to note that a key focus of complex systems
is on the interactions between elements of a system as opposed to the elements
themselves. First I will explain these properties in more detail, and then go on
to explain precisely what is the adaptive part of complex aadaptive systems.
Complex Systems
Non-determinism stems from the number of interactors and hence interactions
in the system. Given that these agents interact in a non-linear fashion, we can
see how chaotic behaviour can quickly emerge in a complex system and hence see
how complex systems are intrinsicly non-deterministic. As an example of how
chaotic behaviour can emerge, consider the quadratic map equation below.[27]
C
n+1
= aC
n
(1 − C
n
)
If we vary the constant a we can radically alter the models behaviour. For
instance, set C
0
= 0.1, and a = 1.5. C
n
tends to 1/3, and then stays there
forever, as shown by the cobweb diagram. This is an illustration of dynamical
systems equilibrium - a fixed point attractor, so called as the equation is pulled
towards this single point in the cobweb diagram. The cobweb diagram plots the
value of the function at n on the x-axis and at n+1 on the y-axis.
If however, we set a = 3.3 we get regular oscillations, which is known as a
periodic limit cycle. Moving a more now, such that a = 3.52 we encounter a
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Figure 2.1: Fixed Point Graph
Figure 2.2: A cobweb diagram illustrating fixed point attractor
Figure 2.3: Periodic Limit Cycle Graph
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Figure 2.4: A cobweb diagram illustrating periodic limit cycle
Figure 2.5: Quasi-periodic Limit Cycle Graph
Figure 2.6: A cobweb diagram illustrating chaotic behaviour of quasi-periodic
Limit Cycle
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more complex pattern - oscillations within oscillations, known as a quasi periodic
limit cycle. Finally set a = 4 and we reach chaos. This will never actually repeat
itself, however, the system is bounded - it will never move out of the range 0 to
1.
As shown, these systems are very sensitive to initial conditions, and in ad-
dition are path dependent (the previous state is needed to calculate the next
state). These two factors make these systems difficult or sometimes impossible
to predict, even if the initial conditions are exactly known.
In addition complex systems often exhibit emergent behaviour - that is to
say they may have properties that can only be studied at a higher level - the
system is greater than the sum of its parts.[20]
Another interesting feature of complex systems is that they contain feedback
loops. This is an example easily related to the economy. Firstly a feedback loop
can either be positive or negative. It is linked to path dependence in that it is
when something of the past effects something in the present. When the event
is part of a cause-effect chain which forms a loop it is said to be fed back in
to itself.[20] An example of this in the economy would be bull markets; when
prices are rising, people believe that price rises are probable and therefore have
an incentive to buy - an example of positive feedback.
The economy is definitely a dynamic system in that it changes over time.
It also exhibits non-linearity in many areas from unemployment figures to the
rate of technological advancement. The dynamics of the economy result from
non-linear interactions between billions of individuals. The behaviour of the
economy is unforecastable except in the very short term and hence we are unable
to accurately predict its evolution - the economy is a complex system. Now we
are convinced that the economy is a complex system, we can ask is it also
adaptive? What is the difference between a complex system and a complex
adaptive system?
A complex adaptive system is a complex system with added capability of
being being able to change and learn from experience. It is the ability of systems
to constantly react and adapt to changes in their environment, or to changes in
the way in which other agents behave.
The economy is both a complex system and adaptive. Billions of people
interact, learn, communicate and generate new strategies, business models and
technologies everyday. The economy is constantly evolving, people cooperate to
achieve goals, share knowledge and this experience, learning and application of
new knowledge is what distinguishes a complex adaptive system from a complex
system.
Evolution is also an important notion in this new perspective of the econ-
omy as a complex adaptive system. The evolutionary process is responsible for
enabling new discoveries contributing to growth in order and in complexity.
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2.3 Evolution
Evolution is an algorithm that searches some space for fit designs. For evolution
to work, certain criteria must be met. There must exist a design space in which
all possible designs are contained. These designs must be able to be encoded
into a schema and a schema reader must exist to decode these designs into in-
teractors (these readers may be endogenous to the interactors). Constraints in
the environment in which the interactors live form a fitness function, rendering
some interactors fitter than others - the criteria for selection. The algorithm
of evolution consists of only three stages - differentiate, select, amplify. Differ-
entiation is rendering different schema into interactors in the environment, and
tweaking interactors. Selection is the selection of fit interactors in the environ-
ment according to the fitness function for amplification. Amplification is the
spread of good designs in the physical environment, making some small changes,
and the occasional big one. In the economy you could hypothesize that business
models are what are differentiated. The market is the selector - bad business
plans don’t survive in the competitive market, and amplification is the spread
of knowledge and imitation of good business plans.
Evolution makes many small alterations and some big ones to the interactors
in the given environment which efficiently searches a massive design space, and
since the selection picks the strong ones, the designs evolve and improve over
time. The economy is therefore adaptive because we learn and experiment with
what we have, searching for most profitable ways of doing things.
It is probably easier to see now why it is so difficult to forecast the economy
over anything but the extremely short term. Sensitivity to initial conditions,
dynamic complexity and path dependence all add to this difficulty. However, as
briefly mentioned, these sort of problems may be better studied using a bottom
up approach which is where Agent Based Modelling comes in.
2.3.1 Genetic Algorithms
2.4 Agent Based Modelling
Agent Based Modelling provides a way of growing artificial societies of sorts.
A key point of the previous section was that although the economy may be
unpredictable and unforecastable, that doesn’t mean economics is a lost cause.
Science is not about simply predicting, but explaining how certain phenomena
emerge from micro interactions. This is exactly what Agent Based Modelling
allows us to do.
.. one must show how a population of boundedly rational (cogni-
tively plausible) agents, interacting locally in some space, could ac-
tually arrive at the pattern on time scales of interest - be it in wealth
distribution, spatial settlement pattern, or pattern of violence. Hence
to explain macroscopic social patterns, we try to grow them in multi
agent models. (Joshua M Epstein, Generative Social Science)[24]
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Agent based modelling involves creating autonomous agents in some space,
in this case an economy, who are heterogeneous and interact with each other
in a decentralised fashion (i.e. through local interactions). In my model agents
will be heterogeneous in how much they can produce of the two goods and later
on also in how much they can remember. By running the simulation I will
be able to observe and analyse any emergent behaviour. It is also important
to note the micro specifications that result in particular macro phenomena are
not definite solutions, moreover they are candidate explanations that prompt
further investigation, especially if there exist multiple micro specifications that
result in a macro structure. In this case it would be necessary to do further
work in order to determine which is the most likely candidate solution. Agent
based modelling is also a tool to subject theories to stress testing. In the context
of my project, relaxing assumptions of neoclassical economic theory could help
deduce whether or not these assumptions are necessary to produce a specific
macro phenomenon.
In the quotation above, it was noted that agents have bounded rationality.
Their rationality is bounded in two ways. Firstly through information. Agents
do not have access to global information (although it is possible to create this
as a network in order to observe any differences it creates). Secondly they are
bounded by computational power, in that it is not infinite.
Many agent based models have proved to be a huge success and the use of
such models is rapidly gaining pace as a way of studying such complex systems.
A good example would be the implementation of a simulation of the Anasazi
society by Dean, Gumerman, Epstein, Axtell, Swedlund, McCarroll and Parker.
In this simulation they attempted to grow a “500 year spatio-temporal demo-
graphic history - the population time series and spatial settlement dynamics of
the Anasazi,”[24] which was tested against empirical data.
This was a society that existed in a valley in Arizona between 800 and
1300AD, but then vanished. The study managed to conclude that it could not
be environmental factors alone that resulted in the demise of the Anasazi - a
huge step forwards for the long search in to what had happened. [23]
2.5 Inspiration
After reading the fantastic paper written by Allen Wilhite titled “Bilateral Trade
and Small-world Networks”[1] I developed a strong interest in his conclusions
and felt that his model would be a good place to start. Wilhite implemented
an agent based simulation in which agents were able to produce or trade one
of two durable goods. His aim was to explore the efficiency of various network
topologies with respect to search, negotiation and exchange. He also experi-
mented to see the effect that the various network topologies
1
(which will be
defined later) had on issues such as the speed and extent of price convergence.
I think his model could be a solid foundation to build on and in addition I
1
The topologies differed in who each agent could trade with. For instance one topology
had agents in disjoint groups and in another every agent could trade with every other agent.
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feel that the report was written well enough for me to attempt to replicate his
work. Therefore, in the next section I will start with my initial model which is
that of Wilhite’s paper. Wilhite went on to write a second paper in 2003 titled
“Self-organising Production and Exchange”[22]. In this paper he introduced
the notion of transaction costs to reflect the cost of shipping and other expenses
incurred in trade. I felt that this was a realistic addition and therefore have also
incorporated this into my initial model.
Wilhite’s work however is not the only work to have had such a strong
influence on my project. In one of the first works at Imperial College London in
the area of complex systems and social dynamics, Kelvin Au did his individual
project in 2005. He implemented a simulation titled “Dynamics of Human
Behaviour: Evolution of Hierarchical Groups”[7]. His report gave extremely
sound explanations on complex systems in a very accessible way and the base of
my knowledge in this area did indeed came from his report. He also had a lot of
work on various frameworks available for simulations and although in the end I
decided to implement it myself it was good to have all of this research integrated
in one document. He also shared the notion of interactions with Gu`erillot.
Camille Gu`erillot wrote an MSC report and completed the implementation
of an agent-based simulation at Imperial College London in 2005. He wrote a
simulation on the “Dynamics of Human Behaviour”[6] which gave me a great
insight in to the complexity of the field. He utilised Au’s technique of using
interactions which has inspired my work. In his model every agent got an op-
portunity to perform an interaction on every iteration. In an interaction, an
agent would engage with a neighbouring agent, resulting in one of several pos-
sible actions.
2
. This notion is reflected in my model described since extensions
will be modelled as interactions - to start with there is just produce and trade,
but later learning can be seen to be an interaction, as can reproduction.
Jie Shen completed an independent study option at Imperial titled “Dynam-
ics of Human Society: Introduction to Multi-Agent System Based Research in
Social Sciences”.[3] His account provided a lot of information on multi-agent
systems and the research being carried out in the area which definitely helped
further my understanding.
2.6 Related Work
Aside from Wilhite’s model, another interesting and notable work was “AS-
PEN”. This was the implementation of an agent based model designed to sim-
ulate the ASPEN economy, documented in the paper “ASPEN: A microsimula-
tion of a model economy”[4]. This employs a Monte-Carlo simulation, in which
agents are designed to be “real-life-economic-decision-makers”. In the world,
households exist who are employed, or alternatively on social security benefits
and strive to earn an income to consume goods or save money. Multiple indus-
tries are modeled through creating agents as firms, and these firms set prices
using a genetic algorithm learning classifier system permitting the development
2
To name a few interactions: Talk, fight, flirt,
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of pricing strategy. In addition, the economy is governed by a single agent, and a
financial sector is modelled. The simulation produced dramatic results, includ-
ing the emergence of business cycles. It’s aim is to be improved and enriched
enough for it to become useful as a forecasting tool.
The simulation documented in this report is far more abstract than that
of the economy of ASPEN. However, the aim is not to create a model used in
forecasting the economy of a small state, moreover, it is an investigation into
the potential of agent-based models as a tool for gaining insight into how trends
witnessed in today’s world might emerge. In fact, the abstraction actually still
allows for some extremely interesting results, emphasising that even the simplest
of models have their contributions.
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Chapter 3
Model
3.1 Introduction
In the background section we established that perhaps a better way to study
economics is through a bottom up approach, something to which agent-based
modelling is well suited. Although the simulation to be implemented is ex-
tremely simple in that there are only two goods and there is no distinction
between individuals and firms, it is hoped that it will allow for some interest-
ing analysis of the assumptions made by Neoclassical theory in terms of their
realism and necessity, and give a realistic representation of wealth distribution.
In addition, employing evolution will allow an insight into the importance of
various attributes of agents in different contexts with respect to the model at
hand.
The model to be implemented is that of a basic economy in the form of
an agent-based simulation. In the artificial world, autonomous agents are able
both to produce and trade one of two durable goods, Good 1 and Good 2.
The simulation is a series of ticks, and on each tick every agent is given the
opportunity to perform one of two actions. An agent is constrained either to
producing one of the two goods, or exchanging one good for another, and each
agent’s action is carried out sequentially. The act of exchange depicts bilateral
trade in that agents swap goods for goods. In the model, Good 2 is infinitely
divisible, acting as money, whereas Good 1 can only be traded in whole units.
Initially the model is simple and agents act in a rational, strategic, myopic
manner insofar as they have a common goal of maximising their utility and do
not try to trick other agents by misleading them. However, as the simulation is
enriched, other aspects such as evolution, learning and a notion of memory will
be brought in. These will be covered in due course but for simplicity, there will
first be an explanation of how the initial model has been implemented and an
evaluation of the findings. From here we will be better equipped to understand
the natural progression and direction of the focus.
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3.2 Initial Model
In 2003, Allen Wilhite[22] implemented a simulation of bilateral trade between
agents in a produce - exchange economy. The initial model is an implementation
of this work since it will provide a solid foundation upon which to build. From
here, extensions will be tried and evaluated, as well as the initial set ups in order
to better understand how the micro interactions of agents may lead to macro
trends. The project, therefore is somewhat experimental and hence abstraction
and dynamism are essential. Attaining technological goals will be discussed
after the model is explained.
First, on each tick or iteration of the simulation, every agent has the oppor-
tunity to produce or trade. An agent is allowed to produce only one of the two
goods or, but not also, trade with another agent on each of his turns, although
he may be picked as a trade partner by another agent. An agent’s decision is
deduced by calculating which action will maximize their utility.
Utility was first introduced by the mathematician Bernoulli; however, the
importance of this revelation went unnoticed for many years. It was only 60
years later that an English philosopher, Jeremy Bentham,[10] independently
discovered this notion. He proposed that pursuing your own best interest did
indeed translate into making economic decisions. He went on to introduce the
measure of pleasure or pain to be one’s utility, a measure in utils. Furthermore,
one would make economic decisions based on maximising one’s utility. It is
important to note however, while Economic theory today tends to regard utility
as an abstraction from pleasure and pain, it is rather an order of preference with
no link to explaining mental processes from which it stems and, in addition is
only a relative measure.[8] Utility of agent i is calculated in the model according
to the Cobb-Douglas Utility Function:
U
i
= g
i
1
g
i
2
, i ∈ {1, ..., n}
where g
1
and g
2
are the amount of Goods 1 and Goods 2 possessed by agent
i respectively and n is the total number of agents.[1]
It is worth noting that this is a symmetric utility function, in that an agent
has no innate preference towards either good. This means that the two agents’
desire for the goods is inherently equal, but deals are available when the differ-
ences between amounts of both goods are apparent across the two agents.
Having established the goal of an agent, let us move on to the next aspect -
production. For production, an agent has a simple unique production function
for each good. An agent may produce r
i
of g
1
and s
i
of g
2
. Formally,
∆g
1
= r
i
; ∆g
2
= s
i
r, s ∈ {1, ..., k}; i ∈ {1, ..., n},
where r and s are randomly determined integers at initialisation lying in the
region 1 to k, and n is the number of agents.[1]
The constant k in Wilhite’s model[1] was k = 30, and this value will also be
used here (although changing it will be possible).
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For trade, otherwise known as exchange, there are three stages: Search, Ne-
gotiation, and Exchange. Search is the act of agent i finding a partner with
whome to trade. At first, m agents will be randomly selected from the set of
agents with whom agent i is allowed to trade. Agent i will calculate his Marginal
Rate of Substitution or MRS as well as the MRS of all of the m agents.
The Marginal Rate of Substitution is the amount of Good 2 an agent is
willing to give up for another unit of Good 1. Using the utility function, the
MRS is given by [1]
mrs
i
=
U
1
U
2
=
g
i
2
g
i
1
where
U = U(g
1
, g
2
), U
1
(g
1
, g
2
) =
δU
δg
1
(g
1
, g
2
), U
2
(g
1
, g
2
) =
δU
δg
2
(g
1
, g
2
) i ∈ {1, ..., n}
A difference between the MRS of two agents is indicative of an opportunity
for mutually beneficial exchange. If this is the case between the searching and
selecting agent, we move on to negotiation. Negotiation is the act of deciding a
price at which to exchange goods and of deciding on the amount to exchange.
The trading price between agents i and j is calculated using:[1]
p
i,j
=
g
i
2
+ g
j
2
g
i
1
+ g
j
1
, i, j ∈ 1, ..., n
Since this price is per unit, the agents will partake in hypothetical trading
to decide the quantity to trade and this ceases when it is no longer increasing
the utility of either of the two agents. Hypothetical trading is necessary since
you want to search through the m agents for the best deal and hence a trade
can’t execute it until all m agents have been reviewed.
In summary, the algorithm of the initial model on each iteration is given
below.
1. Calculate the change in utility you would gain from choosing to produce
Good 1 and commit it to memory.
2. Calculate the change in utility you would gain from choosing to produce
Good 2 and commit it to memory.
3. Calculate your Marginal Rate of Substitution, MRS.
4. From the potential agents you can trade with, select m and for each agent:
(a) Look at the agent’s MRS, if yours and theirs do not differ, disregard
the agent and move on to the next one. If they do differ, continue
with the steps below.
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(b) Calculate the price at which you will trade.
(c) Engage in hypothetical trading until either of your utilities is no
longer increased.
(d) Remember the hypothetical trade and return to step (a).
5. Compare all items in your memory and choose the action which yields the
greatest increase in utility.
6. Execute this action.
3.2.1 With whom can an agent trade?
In the initial model, who an agent can trade with is imposed purely by the
system. However, it would be interesting to allow for the evolution of trade
networks through allowing agents to expand their network of contacts over time.
There are several key contributors to the reason for initially restricting an agent’s
possible trade partners. One is the simplicity of the implementation, making
it easier to verify the correctness of the basic algorithm through employing
minimal complexity. Secondly, it would be interesting to evaluate the evolution
of trade networks with respect to the initial network employed. Finally, in order
to properly evaluate the effect of learning on the running of the simulation, it
is necessary to have a method of comparison - to know the difference with and
without this feature. This will allow sounder conclusions to be drawn from any
changes in macro trends or micro behavior. There will be four networks to
choose from, depicted in the Figures 3.1, 3.2, 3.3, 3.4.
For simplicity, imagine the economy as a set of agents organised as a ring
lattice around the edge of a circle. In a Global Network, Figure 3.1 every agent
can trade with every other agent.[1] In the Local Disconnected Network, Figure
3.2 , each agent is part of a distinct subset of agents, called districts. The subsets
are both disjoint as an agent can only appear in one set, and exhaustive in the
sense that every agent belongs to a set. This network is analogous to an autarky.
This simply means it does not take part in “international” (cross district) trade
- it is a closed economy. Finally, the Local Connected Network, Figure 3.3 and
the Small-world Network, Figure 3.4 are crosses between the Global and Local
Disconnected networks. The number of agents together with the number of
sets will be configurable. It is also worth noting that the m agents selected
as potential trade partners will be randomly selected in the initial model since
there is no notion of memory.
Having established an understanding of what interactions occur between
agents and the various contexts in which they do so, let us now evaluate the
findings of the initial model. The evaluation is based on the running of 10
simulations (of each set-up), varying the initial conditions. Upon completion of
a simulation, a PDF document is generated. This contains data on macro trends,
specialisations, and the strategies of particular agents. It is the comparison of
these outputs that is the basis for conclusion on the legitimacy of the model with
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Figure 3.1: Global Network
Figure 3.2: Local Disconnected Network
Figure 3.3: Local Connected Network
Figure 3.4: Small-world Network
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respect to the real world, gaining insight into the impact of initial conditions on
the evolution of the simulation, and any limitations that the model presents.
3.3 Evaluation
There are several key questions that shall be addressed throughout this section
- namely:
• Is there price convergence?
• Is there a difference in the dispersion of prices for the different initial
network topologies?
• Is there specialisation in what an agent chooses to produce (or purchase)
or specialisation concerning with whom they choose to trade?
• How do topologies effect the distribution of wealth in societies and is this
distribution similar to that of the real world?
3.3.1 Prices
In every round, every agent has the opportunity to search through all agents in
their district in order to locate a trade partner. As such, the topologies lie on
a continuum between two extremes. On the one hand, in the Global Network
every agent can trade with any other agent, and on the other, in the Local Dis-
connected Network agents are constrained to being able to search through only
a subset of the entire population of agents. As a result, from the simulations
run, it was clear that the dispersion of prices differed across network topologies.
Prices were measured in terms of the amount of Good 2 you would give up for
one unit of Good 1, thus the price refers to the price of Good 1. In the Global
Network, dispersion, measured as the standard deviation of the average price,
was fairly low, on average the deviation was 0.024 (see Figure 3.6 for price over
time). This is best explained by the fact that since every agent is able to search
through the entire population to find an optimal trade partner, there are few
trades that go unrealised. However, in the Local Disconnected network the op-
posite is true. The isolation of traders means that there are many opportunities
for trade that are missed, and although each district converges to an average
price with little deviation, the global standard deviation is approximately 3
times larger than that in the Global Network. A great illustration of just how
much deviation from the global average price is possible, can be seen in Figure
3.5.
Let us now consider the topologies that lie in the middle. The Local Con-
nected and Small World Network differ in that although trade occurs locally
within districts, certain agents are made to be bridges between districts, or
“crossover agents”. In the Local Connected Network however, the crossover
agents only overlap with a neighbouring district, and they also only overlap
with one other district even if there are multiple crossovers. This means that
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Figure 3.5: Illustration of price convergence in a Local Disconnected Network
although the majority of trade occurs locally between agents, goods can prop-
agate through the network and spread globally. This gives lower search costs,
since agents can only search through a subset of the population, but on the
otherhand means that the average path length between agents is increased from
the Global Network. This would suggest that not only convergence would be
slower, but also the dispersion of prices should lie somewhere between the two
extremes of the Global and Local Disconnected Network topologies. In fact,
the difference between the deviation from the average price was only marginally
different from that of the Global Network as shown in Table 3.1. In addition,
the speed of convergence was also fairly close. As for the Small World Network,
the dispersion was lower still (see Figure 3.7). It seems that the continuum of
network topologies does not correlate linearly to the difference in prices across
topologies. This shows that there is some efficiency in both the Local Connected
and Small World Networks. Even though the path lengths for goods to reach
an agent is increased, the cost of search is greatly reduced relative to the Global
Network, and this reduction does not make a very significant difference on price
dispersion. This gives rise to further investigation, and the topic of network
efficiency will be covered in Chapter 6.
Contrary to the Neoclassical view of equilibrium, I found that prices did
not converge to a single uniform price. However, the oscillation of prices did
dampen considerably with time across the simulation. At first, prices (the
amount of Good 2 an agent would be willing to give up for one unit of Good 1)
fell within the average range of 0.5 and 1.5. By approximately 150 iterations,
this fluctuation had reduced to between 0.85 to 1.1, and by 1000 iterations, it
had reduced further to, on average between, 1.05 and 0.95. These were taken as
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Figure 3.6: Illustration of price convergence in a Global Network
an average over 10 simulations of the Global Network with 400 agents, running
for 2000 iterations. The Global Network was chosen since it best coincides
with the Neoclassical assumption of perfect information - being able to search
through every agent in the population.
Recall the Neoclassical view of price equilibrium was rooted in the first law
of thermodynamics, stating that if energy is conserved, then the system is guar-
anteed to reach an equilibrium. It was thought prices would reach equilibrium
unless an exogenous force was to shift it from this equilibrium. In the simula-
tion, the reason for price fluctuation is entirely endogeneous to the system; it
was the production of goods by actors in the economy that caused persistent
price fluctuations.
Let us now address the reason for the continuous fluctuations in prices. It
seems to stem from the possibility of production. Since agents often chose
to produce, the stock of goods changes frequently which in itself prompts price
adjustment. Although prices did fluctuate, it was always within a clearly defined
range. This is common in the real world, especially with commodities where
the amount being produced is not consistent. For example agricultural products
often suffer potentially damaging price fluctuations. This can be due to poor
crop yields stemming from weather, disease and so on, or to restricted supply,
or to over production leading to insufficient demand for the quantity produced.
Full details of average prices and standard deviation, averaged over 10 sim-
ulations, each with 400 agents and 20 districts with only 2 crossovers (if appli-
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Figure 3.7: Illustration of price convergence in a Small World Network
cable) are given in Table 3.1.
Topology
Price
Standard Deviation
Local Disconnected 0.948
0.08
Local Connected
0.958
0.03
Small World
1.01
0.03
Global
0.935
0.024
Table 3.1: Table showing average and standard deviation of prices with different
network topologies
3.3.2 Specialisation
Throughout the simulations that were run with the initial model, a common
theme emerged. The ratio of production to trade was highly skewed towards
production. This is shown by looking at the percentage of agents who specialise
with respect to the interaction they perform most frequently - production or
trade. In Wilhite’s paper, [22] he categorised agents on a continuum. At one
end of the spectrum are pure producers, agents who choose to produce at least
99% of the time. On the other end are pure traders. Similarly, these are agents
who choose trade at least 99% of the time. In between lie the heavy producers
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Figure 3.8: Continuum of specialisation with pure producers, PP, to pure trades,
PT, with 0% to 100% trade
Topology
Pure Producer Heavy Producer Heavy Trader Pure Trader
Local Disconnected
43.7%
55.3 %
1%
0%
Local Connected
43.4%
55.5 %
0.8%
0.3%
Small World
47.9%
50.6%
1.3%
0.2%
Global
48%
50%
1.4%
0.6%
Table 3.2: Percentage of agents in each category with respect to network topol-
ogy
and heavy traders. These are agents who produce or trade, respectively, more
than 50% but less than 99% of the time. An illustration of the continuum is
shown in . The continuum can be viewed as illustrating extents of specialisation,
with extremely high specialisation at either end, and little specialisation towards
the centre.
Before discussing the degree of specialisation, if any, across the agent pop-
ulations it is perhaps important to establish why this is of use. By seeing if
agents do specialise, it is possible to learn about the model. The strategies that
agents develop of their own accord in order to become optimal operators in the
economy (with respect to their own potential and not a global optimal) become
apparent. By examining what decisions are made on a micro level, it is easier to
infer why these decisions are made, and hence better prepared to answer exactly
why certain macro trends occur, whether or not the model is realistic and also
to gain insight to any shortcomings of the model.
As may be expected given the above, the majority of agents fall in to the
pure and heavy producer categories, shown in Table 3.2. In addition, it is often
the case that agents with the highest utilities are also, more often than not,
in these categories. Let us therefore consider what it is about production that
is so much more appealing than trade. Why is it that, the majority of the
time, even when an agent can search through all other agents, are there so few
opportunities in which trade proves to be more beneficial than production? Is
this really a realistic reflection of the world we live in?
In the model production involves no sacrifice. An agent simply adds to the
stock pile of one of his goods - he give up nothing but time, the same amount
of time another agent gives up for trade. With trade however, an agent gives
away a stock of one good in exchange for a stock of the other. The benefit is
only really presented when the quantity of goods you possess is heavily skewed,
and since utility is calculated to be the multiplication of your stock of goods,
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agents are inclined to keep the stock of their goods similar to maximise utility.
Put differently, the symmetry of the Cobb-Douglas utility function results in
“balanced consumption” leading to greater utility.
The effect of topology on the percentage of agents falling into each category
is fairly small. In Local Disconnected networks, the percentage of agents falling
in to the pure and heavy traders category is reduced by approximately a quar-
ter, illustrated in Table 3.2. This is most likely due to the fact that knowing
fewer people reduces the probability of someone in your district being a suitable
trade partner. What is interesting however, is the fact that there is so little
difference between the number of traders in the Small World, Local Connected
and Global Networks. This is illustrative of the fact that the links provided
by the crossover agents in the Local and Small World Networks allows for flow
of goods around the network, and are of little hindrance to the realisation of
trading opportunities.
Also worthy of note is the relative rush of trades at the beginning, consistent
across all network topologies. Figure 3.9 illustrates this rush, and, as shown,
the number of trades falls fairly rapidly at the beginning (the range falls by
an average 50% within the first 500 iterations
1
) and levels off for the dura-
tion of the simulation to a range of (on average) 10.7 to 5 trades per iteration.
This is a significant fall and its explanation brings us back to Pareto. When
the simulation begins, there are many trading opportunities due to the uniform
distribution of goods - their endowments. Feldman showed when studying equi-
librium characteristics of bilateral trade, [1] that as long as the agents are in
possession of more than 0 of one of the commodities, that the pairwise optimal
allocation is also a Pareto optimal allocation. That is to say that by selecting
pairs of agents to trade, upon reaching a steady state, no more trades could
occur that made both parties better off. However, in the model there is a twist.
The optimal allocation of resources changes with time due to the possibility
of production. Therefore, opportunities for trade are more prominent in the
beginning, but as people exhaust those opportunities, the balance of goods and
allocation of resources is optimised and there becomes little room for mutually
beneficial exchange (as explained previously). However, it is important to note
that the trades are not reduced to 0. This is due to the fact that trades are
occasionally made more beneficial than production as the stock of goods of some
agents become more skewed, since, as we know there are some pure traders in
the economy. If we began with a finite set of resources, (if, for instance, produc-
tion weren’t possible) as the steady state is explained in Neoclassical economics,
we would reach a point where no more trades were possible and this point would
coincide with the point at which a price equilibrium is reached. This is not the
case. Production means that thre are continuing trade opportunities that prove
to be more beneficial that production (although they are, admittedly, few) and
accounts for fluctuations in prices.
Let us consider the contributing factors to the emergence of this specialisa-
tion. What distinguishes agents who specialise in production and trade? The
1
This is an average over 10 simulations of the Global Network.
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Figure 3.9: Trades over time for a Local Connected network
answer to this is the production functions of the agents. Agents develop repet-
itive strategies that they employ in the simulation based on their production
functions that allows them to reap the maximum benefits of what they have
been given. It is possible to profile the agents that fall in to these categories.
Producers
These are the agents who have high production functions. They are well equipped
in the economy. Production virtually always offers better results than trade.
They can be seen as the self sufficient sector of the society.
Often these agents simply alternate in the production of the two goods,
keeping their stock piles close together and enjoying an easy life with high
utility. The majority of the time, this is a one-period cycle - they produce Good
1 then Good 2 and so on. These agents often never initiate trade. Furthermore,
they are not even picked by others as trade partners. An illustration of the
movement of goods for a self sufficient agent is shown in Figure 3.10.
Self-sufficiency is not the only strategy of pure producers and also was shown
not to be the best. Some agents were particularly proficient in production of
only one of the goods. They specialised even further in that not only were they
pure producers, but they also only produced one of the goods the majority of the
time. On average, the good that they were most proficient in would be produced
97.5% of the time. What is interesting is the dependence of these agents on
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Figure 3.10: A close up of the movement of goods for a self sufficient agent,
showing alternation between production of each good
the need of other agents to trade with them. They never initiated trade, but
their position meant they were good candidates for many other agents who
lacked production proficiency in the good they were producing. This strategy,
on average, was apparent in approximately 22.7% of the pure producers. These
producers were the consistently the most wealthy agents in the simulation. This
is probably due to the fact that they achieved exchange without having to give
up the opportunity to produce. Their balance of goods became closer because
others initiated trade with them. In a sense, they could exchange for free because
they didn’t have to give up time.
The general profile for heavy producers was agents who still had skewed
production functions but often neither production ability was particularly poor
(ranging from 10 to 23 for those with the highest utility). These often produced
the good they were proficient in for a number of rounds, and then trade for the
other good before falling back to production. In addition, they had on average
a third of the number of agents initiating trade with them compared to the pure
producers who specialised in the production of one good.
Traders
Pure traders generally spent 100% of their time trading. They typically had ex-
tremely low ability in production (ranging from 1 to 7 for those with the highest
utilities) and their wealth was unequivocally lower than the producers. Due to
their poor production capability they often made margins through purchasing
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Figure 3.11: Illustration of the movement of goods for a pure trader
goods in one round and selling in the next. Although they frequently initiated
trade, on average no agent initiated trade with them. Their lives were bleak,
and they were the poorest of the agents, but trade was the only way of survival.
Pure traders didn’t specialise in the good they chose to buy. They, like the pure
producers, switched between buying and selling Good 1 from round to round
giving a 50/50 split. An illustration of the movement of goods for a pure trader
is shown in Figure 3.11
However, they too specialised further not in what they traded but in with
whom they traded relative to the heavy producers and traders. On average in
the Global Network, out of 1000 trades, there would only be 66.2 distinct trade
partners out of 400 possible trade partners. This shows that pure traders had
“regular clients” in that they would repeatedly return to the same agents to
trade.
Heavy traders also often suffered similar poor ability in production, although
this was skewed and hence they, like heavy producers, would have one round of
production and then several rounds of trade.
Effect of topology
Table 3.2 shows that although the Global Network has the most trades out of all
the topologies, it actually also has the most pure producers. It seems that as the
topology restricts the number of agents known, more agents migrate categories,
from the two extremes of specialisation, pure producers and traders, to the
middle of the continuum, heavy producers and heavy traders. It is easy to see
there are fewer pure traders in the topologies other than the Global Network.
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It is not feasible for agents to find a suitable trade partner (one which makes
trade more profitable than production) in every round when they are only able
to search through a small subset of the population. However, it is less easy to
understand why the number of pure producers is considerably lower in the Local
Connected and Disconnected Networks relative to the Global and Small World
Networks. The most likely explanation is to do with competition in the market.
In the simulation the notion of competition relates to the fact that the more
agents with whom one must compete for a trade partner, the more likely it is
that the deal will be taken by another agent. This means that an agent who
could have been a good trade partner now has a better aligned stock of goods for
maximising their utility, so trading with certain formerly useful agents is now of
no use to them. The Small World Network and Global Network offer the most
competition in trades. In the global network, every agent searches through every
other agent and therefore the chance of a trade being made that jeopardises
another agent’s opportunity to trade is high. In the Small World Network it is
slightly more complicated. In Small World Networks a district can be connected
to any other district, or more than one if there are multiple crossover agents.
This means that competition across districts is higher as more crossover agents
compete for the best trades. Therefore, crossover agents may actually have
difficulty exploiting their position because often all the optimal trades are gone
and therefore they are more likely to become pure producers. Notice that in the
Local Connected Network there are far more heavy producers. It is important
to be aware that this change is not purely the result of competition. It is
a combination of competition allowing crossover producers to have occasional
extra trade, and of the network being more restrictive, therefore encouraging
pure traders and heavy traders to move to production - something not exclusive
to crossover agents.
This has the knock on effect that since they are no longer bringing in good
deals for local agents in their district, they too are more inclined to succumb
to production. Therefore, open networks lead to more trade, but also to more
extreme specialisations, since competition in the world increases. On the other
hand, in the Local Connected and Disconnected networks, the lack of competi-
tion actually leads to less extreme specialisation since opportunities are available
more of the time for some agents, although globally it leads to fewer trading
opportunities. This is an interesting observation as it is illustrative of the con-
nections between macro and micro trends which may seem superficially to be
in opposition to one another but which are not in fact mutually contradictory
and between which there are elements of causality and symbiosis.
3.3.3 Wealth
Wealth and its distribution are important indicators of the extent to which
reality is captured in the model. This can also be related to countries of todays
world, and serves as an indication of allocation of resources, poverty, flaws in
policy and so on. Its importance is a reason to investigate how this evolves
through the simulation and why.
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Let us first establish what wealth is in the simulation. Wealth is measured as
the value of assets minus the value of liabilities. Since in this model liabilities,
or debt, do not exist, wealth is simply the value of the stock of goods held at
one time. This leads to the need for a definition of what is meant by value in
the context of the model. Since prices are measured in terms of how much Good
2 an agent would be prepared to give up or pay for one unit of Good 1, it is fair
to say that the value of an agents assets is:
w
i
t
= p × g
1
+ g
2
where w
i
is the wealth of agent i at time t
g1, g2 is the stock of Good 1,
or Good 2 respectively for agent i at time t,
p is the average price of Good 1
at time empht
Having defined wealth, let us now identify what and how to evaluate the
distribution of this wealth. Firstly, it would be interesting to see whether the
global distribution of wealth differs across topologies, and also if the wealth
of districts varies across topologies. To do this, however, some sort of index
reflecting wealth distribution is necessary.
Such an index does exist, and is called the Gini Coefficient. It is a measure
of inequality that can be applied to both wealth and income. Its values range
between 0 and 1; 0 represents perfect equality - where all agents have the same
wealth, and 1 perfect inequality - all agents have no wealth except for one agent
who has all of the wealth.
In order to understand how the Gini Coefficient works, let us first introduce
the Lorenz Curve. An example of the Lorenz Curve can be seen in Figure 3.12.
[26] As is evident from the graph, the Lorenz Curve plots the percentage of
households (in this case agents) against the percentage of income (in this case
wealth
2
). In the context of the simulation, it says for example, 10% of the
wealth is in the hands of 30% of the agents. Perfect equality is shown simply as
the line of “y = x”. This can be understood to mean that 20% of the wealth is
in 20% of the agents hands, or 21% of the wealth is in 21% of the agents hands,
or, more simply, everybody has the same wealth. Perfect inequality is shown as
the blue line. Since the Lorenz Curve illustrates the cumulative distribution of
wealth, the line of perfect inequality stays at 0 until the final, wealthiest agent
is cumulatively included. At this point it jumps up, showing that 100% of the
wealth is in the hands of a sole agent.
The Lorenz Curve can be computed directly from the data held in the simu-
lation, making it a simple yet telling method of analysis. The Gini Coefficient,
however, is slightly more complex. Take the area of the triangle under the line
of perfect equality to have an area of 1. The Gini Coefficient represents the
proportion of that area that lies between the line of perfect equality and the
Lorenz Curve, labelled Gini Index in Figure 3.13[16].
2
Although is wealth differentiated from income in that wealth is a measure of assets and
income a measure of inflows and outflows, the Lorenz Curve as well as the Gini Coefficient
can be used to assess the distribution of both.
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Figure 3.12: An Illustration of the Lorenz Curve
If the area under the Lorenz Curve is B, and the area above (but below the
45 Degree line) is A, then the Gini index corresponds to A/(A + B). Since A +
B = 0.5, G = 2A = 1 - 2B. Since B is the area under the Lorenz Curve, if its
function is known, the Gini Coefficient can be found by integration.
G = 1 − 2
∫
1
0
L(X)dX
However, in the context of this simulation, it is infeasible to determine the
function of the Lorenz Curve, so instead a method of calculating the Gini Co-
efficient directly from data will be used.
For a random sample S, with values y
i
, i = 1 to n, indexed in increasing order
(y
i
≤ y
i+1
) we can compute G(S), a consistent estimator of the Gini Coefficient
to be:
G(S) = 1 −
2
n − 1
(
n + 1 − 2
(∑
n
i=1
(n + 1 − i)y
i
∑
n
i=1
y
i
))
By a consistent estimator, we simply mean one which converges in probabil-
ity to the true value of the parameter as the sample size is increased.
Having established a way of assessing the distribution of wealth, let us move
on to see the distribution found in the initial model. Across the different network
topologies, there was only a small difference in the distribution of wealth -
measured as the Gini Coefficient. This is illustrated in Table 3.3. This small
difference across varying topologies called for a test into its significance in order
to determine the probability of a measurement occurring by chance. Since it
is necessary to compare 4 samples, it is not appropriate to use a test statistic
such as the t-test. Not only would it increase the amount of computation, but
in addition, the type one error rate rises with the number of tests we perform.
A type one error refers to a false rejection of a true null hypothesis. Instead
I will use the ANOVA test, a generalisation of the t-test to cover more than 2
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Figure 3.13: Diagram indicating the Gini coefficent
groups, with a hypothesis H
0
that the means do not differ, and H
a
that they
do.
In order to perform the test, the following steps are taken:[32]
1. Calculate the sample average for each group
2. Calculate the average of these averages, ¯x
3. Calculate the sample variance of the averages, S
∗2
4. Calculate the sample variance of each group
5. Calculate the average of all sample variances, S
2
6. Calculate the F Statistic:
F =
nS
∗2
S
2
where n is the number of items in a group.
The F-Statistic is 0.3, which is well below the necessary threshold, meaning
that it is not possible to reject the null hypothesis that the means are equal.
This in turn means that the topology does not have a statistically significant
effect on the global distribution of wealth. Perhaps it is again a question of
the lack of necessity and benefit in trade. Since most agents are self-reliant,
the problem of redundancy of network topology is presented. In essence, it is
not possible to make proper comparisons based on topology due to the lack of
influence it has on the evolution of the simulation, since production does not
require a network.
However, in spite of this, it is possible to see the effect of network topology
in closing the gap of wealth across districts. Figure 3.14 shows the wealth per
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(a) Wealth in a Local Disconnected Network
(b) Wealth in a Small World Network
Figure 3.14: Wealth With Time
Topology
Gini
Local Disconnected 0.183
Local Connected
0.195
Small World
0.192
Global
0.186
Table 3.3: Average Gini Coefficient across topologies
district of a Local Disconnected Network, and of a Small World Network. It is
clear to see that the wealth in a district is affected by topology when the prices
used to calculate wealth are average prices per district rather than global ones.
Although it would be possible to compute the Gini Coefficient on a per district
basis, the lower number of agents involved in the calculation can result in the
Gini Coefficient becoming extremely skewed, hence graphical analysis was used
instead.
3
The differences seen are indicative of the fact that allowing goods
to propagate globally through the network leads to more even prices and hence
more even value of goods, which in turn leads to less differentiation between
districts based on wealth.
Having established that the Gini Coefficient - the measure of inequality - is
not significantly different across topologies, it is necessary now to ask whether
the value correlates to the real world. In short, it does not. This self-reliant
world is a picture of harmonious equality. It does not correlate to values we
witness in life. In reality, Gini Coefficients rarely fall below 0.25 for income
distribution, which is almost always lower than wealth distribution. Countries
such as the UK generally fluctuate between 0.3 and 0.4, and the USA 0.3 to
0.5. In reality, wealth distribution tends to follow a Pareto distribution. This
3
Although the Gini Coefficient could be computed for each district by having more agents
per district, my focus lies more in the global distribution of wealth than the local, since this
global focus is more closely related to development in economies which will be discussed later.
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is sometimes known as the Pareto principle or the 80-20 rule which says that
80% of the wealth is controlled by 20% of the population.
4
From simulations using this model, the Gini Coefficient rarely reaches above
0.2. Although the initial endowments and production functions have a uniform
distribution, it would still be hoped that the Gini Coefficient would have evolved
to become more realistic. Simulations of 20000 iterations were conducted to
check that the simulations were being run for a sufficient length of time, but
little changed and in some cases the Gini Coefficient even decreased. This must
be investigated further prior to being able to suggest why this might be the
case, and will indeed be a topic in Section BLAH.
3.3.4 Conclusion
The initial model paints a world in which production is largely optimal. An
agents fortune is determined simply by his proficiency in the production of
goods. The graph in Figure 3.15 illustrates the small amount of trade apparent
in the simulation, with the largest average percentage of trade being just 3.4%.
However, it is also clear that as we move from the autarky to the Global Network,
there is a clear trend of increasing trade. This again highlights the importance
of “open borders” in allowing the realisation of trading opportunities. However,
despite this correlation, the amount of trade is still extremely low, so low that
it is difficult to evaluate much regarding networks and the impact of crossover
agents.
Figure 3.15: The percentage of trade across different network topologies, aver-
aged over 10 simulations of each sort.
The model offers insight into the reasons for emergence of specialisation. It
allows agents to be characterised by the strategy they adopt and offers sound
conclusions as to what causes certain strategies. The specialisation in the model
is not unlike the way the world works. People (or companies, and even countries)
4
The Lorenz Curve is actually a function of the CDF of the Pareto distribution.
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produce what they are most proficient in producing. This is not only reflective
of a capitalist economy, but is also an argument for increased efficiency with
globalisation. By widening the scope of people with whom agents interact, it
is possible to achieve opportunities in efficiency that would not be possible in
isolated economies (such as the Local Disconnected Network). By widening
this scope, the poorest agents, who are generally pure traders, can nonetheless
increase their wealth by a factor of 2. Open borders or open trade allows the
specialisation of agents - it allows pure producers to rely on demand for their
goods and traders to rely on supply by a larger number of the population. It is
the ability to specialise, as Adam Smith noted in his discussion on the division
of labour, that contributes to greater efficiency.
However, the distribution of wealth realised by all networks was incompara-
ble to anywhere in today’s world. This conflict with what is witnessed in reality
is worthy of investigation. In addition, it is difficult to judge how the network
topology affects trade and the spread of goods when the vast majority of agents
produce, hence the networks are almost redundant. Since the importance of
topology in the study of complex systems cannot go unnoticed, trade must be
increased in order to delve deeper into the effect of topology on efficiency, global-
isation, allocation of resources and hence wealth distribution. One of the major
downfalls of economics is the tendency to be concerned more with the actions
of individuals than with the interactions between them. This is contrary to the
view of complex systems research, where it is considered that a key point of in-
terest is the interactions between elements of a system, and the structure of the
network of interactions as opposed to the elements themselves. In this context
the cooperative interaction (so far) is solely trade and the structure is the topol-
ogy imposed on the system. To gain insight into the robustness and efficiency
of these networks together with their emergence, trade must be increased. Not
only is this necessary for proper evaluation, but it is also of fundamental impor-
tance if we are to progress in a direction that better reflects macro trends that
are witnessed. It is not the case that the vast majority of us are self-sufficient;
we do not farm our foods and do not make our own computers. In reality, pro-
duce comes from a few wealthy, able firms who are proficient in the production
of a certain good. Another thought is that wealth increases linearly and so does
the stock of goods. Perhaps this influences the convergence of prices over time
- in reality efficiency decreases cost and hence (for many industries) prices for
consumers, and excess demand or restricted supply cause price rises. Perhaps
consumption of goods could influence the trend of prices over time.
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Chapter 4
Increasing Trade
4.1 The Method
The world of production stemmed from the fact that the sacrifice involved in
trade decreased its benefit relative to surrender free production. However, we
also know that the symmetry of the Cobb-Douglas utility function means that
the goal of maximizing utility is best achieved by not only increasing the stock
of goods, but also balancing out the stock of goods owned. I needed to find
a simple way of tipping the scales to favour trade more frequently, whilst still
retaining or even increasing the similarity to the world we live in.
The answer is to restrict the production of both goods. To do this, I per-
mitted a configuration option in which you can specify the percentage of agents
who are able to produce both goods. For this subset of the population, half
would be able to produce only Good 1, and the others only Good 2. The result
of doing so is really quite astounding. It is important to note that an agent may
be able to produce neither of the goods. This was allowed since I believed it
would be interesting to introduce some true merchants that must make a living
solely through price arbitrage.
An important question is whether or not this better reflects reality. I believe
yes. It is easy to see that it is not the case that everybody is able to produce
everything and some people can’t produce anything. In industry for instance,
companies specialize. A trainer making company does not manufacture bottled
water on the side. Although the simulation does not model firms, it is fair to
say that not all agents should have expertise in the production of both goods.
By restricting the number of agents who do have expertise in both goods, we
create an inherent demand for these goods - trade is necessary for some agents.
So not only will it paint a better picture of reality, but it will also allow us to see
how the various topologies cope with this new load. In addition it will provide
an opportunity to see if there are benefits to being a crossover agent in this new
world.
In this chapter I investigate the effect this alteration has on the evolution
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of the simulation, including the effect on wealth distribution, specialisation and
price dispersion. In addition, the trends exhibited in varying the percentage of
agents who are able to produce both of the goods will be studied and evaluated.
4.2 Evaluation
The percentage of agents who were able to produce both goods was incremented
in 10% intervals, from 0% to 100%. For each interval, 10 simulations were
run of the local disconnected, local connected, and small world networks. The
global network is excluded herein since it’s results are extremely close to that
of the small world and local connected network, however, it’s search costs are
massively increased. This unrealistic and extremely costly topology is therefore
of little use in relating to the real world, and due to time constraints, no further
investigation into this structure will be carried out.
The following section is divided into 2 areas. One evaluates the effect of
increasing trade on macro trends such as prices and wealth, the other takes
a more detailed look at the specialization of agents that could lead to these
phenomenon.
The aim of restricting who could produce both goods was to facilitate an
increase in trade - to make trade more appealing than production. Perhaps
then we should first assess whether or not this worked. In fact, from 100% to
0% trade was increased 10 fold - it was a success. In addition, as the graph in
Figure 4.1 shows, this increase wasn’t linear as may have been expected.
Figure 4.1: Decrease in trade as the percentage of agents able to produce both
goods decreases
To better understand this trend, it is necessary to clarify precisely why this
restriction lead to more trade in the first place. Recall that the symmetry of the
Cobb-Douglas utility function means that balanced stocks of goods maximizes
utility for agents. Therefore agents will try and keep their piles of goods as equal
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as possible. This in turn means that even if they are proficient at producing
one of the goods - say Good 1, eventually acquiring Good 2, even if it means
sacrificing some of your Good 1 will lead to a higher gain in utility as it will
lead to more balanced stocks. Therefore, if an agent can’t produce Good 2,
eventually it will need to trade for it.
However, the non-linearity is indicative of the fact that the more agents that
are in a “worse” position, the more trading opportunities exist for these agents.
However, after careful analysis, it was clear that this increase in trade was not
happening through all agents simply beginning to trade, and this is discussed
in the following section on specialization.
4.2.1 Inspecting Agent Behaviour
Specialization
The breakdown of how agents specialize is probably one of the most interesting
results from increasing trade. Recall the four categories, pure producers and
pure traders, agents who produce or trade respectively more than 99% of the
time; and heavy producers and traders, agents who produce and trade more
than 50% but less than 99% of the time. You would expect that pure and heavy
producers move to the pure and heavy trader categories as the percentage of
trade increases. However, this is actually not the case.
Figure 4.2: Change in percentage of heavy producers as the percentage of agents
able to produce both goods decreases
Recall that pure producers and traders were the most specialized with re-
spect to the action they performed most frequently. In fact, when the amount
of traders able to produce both goods is low, agents move to the two ends of
the continuum of specialization. The percentage of agents that fall in to the
heavy producer category decreases consistently for all network topologies as the
percentage of agents able to produce both goods moves to 0%. This is shown
in Figure 4.2.
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Figure 4.3: Change in percentage of heavy traders as the percentage of agents
able to produce both goods decreases
As for heavy traders, all topologies (although at different times and to vary-
ing degrees) experience an increase in the percentage of heavy traders to a
maximum point before beginning to decrease consistently up to 100% as illus-
trated in Figure 4.3. Also note that this category seems to show the larges
variance between topologies, however it is important to note that the range of
percentages is around 2% thus the differences are exaggerated on the scale.
Interestingly, the percentage of pure producers decreases as the percentage of
agents able to produce both goods increases up until approximately 80% when
it begins to decline (although at a much slower rate). The percentage of pure
traders decreases sharply, before increasing two fold at 22%, and then decreases
again at just as sharp a rate until the proportion of agents unable to produce
both goods reaches 100%. The graphs for pure producers and traders can be
seen in Figure 4.4 and 4.5 respectively. Notice also that the pure trader category
is subject to the least variance between topologies.
Now the trends have been established, a few more tricky questions to deal
with have emerged, and the following seeks to explore candidate solutions to
these questions. The questions to be addressed are:
• Why is the number of pure producers increasing?
• What prompts agents to become more specialized?
The fact that the number of pure producers falls as more agents can produce
both goods is interesting since the overall amount of trade is decreasing - and
pure producers often never trade. At the 100% threshold we characterized pure
producers as falling in to one of two categories. Those who alternated between
the production of the two goods in a one period cycle, the self sufficient sector.
There were also those who were proficient in the production of only one of the
goods. These virtually always produced the good they were proficient in, and
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as such, would often make great trade partners. These agents relied on the need
of other agents to trade with them. They did not sacrifice their time to trade,
they didn’t need to - someone was always willing to trade with them. This fact
actually permits answering the first two questions in tandem.
As the amount of agents able to produce both of the two goods decreases, sev-
eral divides emerge. Firstly we have the divide between agents who can produce
both goods, one of the goods, and neither. Obviously those who can produce
neither (few and far between) have no choice but to become “shipppers”. They
make a living by buying cheap in one round, and selling dear in the next. In
effect they play the market. However, why do we have less heavy producers and
traders and more pure producers and traders? If you recall, heavy producers
and traders were characterized by producing or trading for a few rounds and
then executing a trade, or producing for one round respectively. Since there
were very few heavy traders in the first place, and virtually 0 when no agents
were able to produce both goods, the changes in this category have little effect
on the overall trend, hence the focus instead lies with the heavy producers. So
it is necessary to explain only why being a heavy producer becomes so rare.
Figure 4.4: Change in percentage of pure producers as the percentage of agents
unable to produce both goods increases
It is simpler to understand if you imagine the case when a large percentage
of agents are unable to produce both goods. Agents now only fall into a few
main categories. As mentioned we have “shippers”. In addition, we have agents
who have a low production function for one of the goods. These agents generally
become pure traders. Trade is almost always more advantageous due to their
poor ability in production. We also have agents who are able to produce one
of the goods with medium to high proficiency. Even though these agents can
only produce one of the goods, the demand for goods in trade is far higher, so
they are in a better position to depend on agents initiating trade with them.
This happens more frequently in the small world network than in the local dis-
connected network which is illustrated in the graph by the small world network
line being above the other two. This is most likely due to the fact that trading
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opportunities exist across groups, hence pure producers can rely on demand for
their produce from a larger subset of the population, be it by direct or succes-
sive trades. However, the number of heavy producers falls as some move to pure
production due to the new demand for goods that are only acquirable through
trading, and some move to become pure traders as they can, more often than
not, find a suitable trade partner. Pure producers don’t need as high produc-
tion proficiency in order for agents to initiate trade with them, and pure traders
don’t need as low proficiency in order to make trade more beneficial since more
agents have skewed stock piles so the probability of finding a trade partner is
increased. In essence, the profile or characterization of agents in the extreme
specialization categories changes. By forcing agents to specialize in what they
produce, the dynamics of the simulation change, and this results in changes in
specialization between interactions performed (production or trade).
This said, there are a few interesting points on the graphs worth noting.
Firstly, as briefly mentioned, the percentage of agents who are pure producers
decrease between the 20% of agents being able to produce both goods and 100%,
as shown in Figure 4.4. Before this point, for all topologies, the percentage of
pure producers begins to increase gently. In addition, the orders are reversed.
Before, the disconnected network had the most pure producers and the small
world network the least. This decline is indicative of some form of saturation.
The peak proportion of pure producers has been reached, but this does not
answer why it begins to increase. One possible explanation is that the number
of agents relying on agents initiating trade with them can’t pass this peak at
20% as otherwise there aren’t enough agents in the rest of the population to
support their need for “free exchange”. Thus the agents who aren’t as proficient
producers in one of the goods can no longer survive as a pure producer as the
percentage of agents able to produce both goods decreases from 20% to 0%.
A second interesting point relates to the graph of the pure traders, shown in
Figure 4.5. Here, we have that at first the proportion of pure traders decreases
sharply, and at 80% doubles with just as steep a gradient, before decreasing
again afterwards.
In addition, still looking at the pure traders graph in Figure 4.5, we see that
the effect of topology on the percentage of agents in this category is negligible.
This is most likely due to the fact that trading is still a last resort for agents.
Thus, the topology may effect the wealth of the pure traders, but it has little
impact relative to production functions on who will be a pure trader.
In conclusion, as the percentage of agents able to produce both goods is
decreased, the profiles of agents in each categorization differs, and this is partly
due to how the utility function influences the optimal strategy of agents, but
in addition, due to the new dynamics that emerge as a result of this forced
specialization.
This movement to the edges of the continuum is in fact a better reflection
of reality. We actually have very few industries in which the level of production
and trade is even. Many companies produce goods and make sales, and others
buy goods purely to sell on, such as cash and carries. There are few who both
produce their own goods and buy other goods to sell on. The best example of
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Figure 4.5: Change in percentage of pure traders as the percentage of agents
unable to produce both goods increases
these companies is most likely supermarkets who buy branded goods as well as
having their own brand. However, on the whole, and even in the business models
of supermarkets, there is a clear distinction between merchants and producers.
Thus this trend in the model is quite realistic for the simplicity in the economy
being modelled.
4.2.2 Global Trends
Price Dispersion
The increase of trade had no consistent effect on the prices of goods across popu-
lations. However, the effect it had on the dispersion of prices was dramatic. The
graph in Figure 4.7 shows this trend for each of the network topologies. For the
small world network the standard deviation of prices was relatively consistent
across the different thresholds. The amount of trade still leads to solid price
convergence across all districts, with consistently low deviation. This highlights
the efficiency in goods spreading globally through the network even when the
amount of trade is high, and the stock piles of goods more inclined to become
uneven. Since the path length is short, goods can reach every agent quickly and
hence there are few trades between groups that go wanting, thus the range of
prices is lower. In contrast, in the local disconnected network an increased need
for trade and thus an increase in trade, leads to many opportunities between
groups that are not realized. This forces the prices between groups further
apart. This is shown in Figure 4.6
For instance, in one district perhaps there are many agents who can not
produce Good 1. Therefore the price is excessively high, since the demand for
Good 1 is far higher. This district is unable to trade with another district
where the price of Good 1 is low, and therefore the gap exists. This could
explain why the increase in trade leads to sharp increases or decreases in prices
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Figure 4.6: Illustration of huge price dispersion at the 100% threshold for the
local disconnected network
across districts. Although this accounts in the increase in price dispersion, an
interesting point on the graph in Figure 4.7 is the point at which standard
deviation in the local disconnected network plummets from 0.37 to 0.21. This
occurs when the change in the percentage of agents able to produce both goods
increases from 40% to 60%. Past 60%, it plateaus, before falling again. It is as if
40% is a threshhold, after which the combination of the demand for goods only
acquirable through trade, and the autarky imposed by the local disconnected
network result in a massive increase in standard deviation, or price dispersion.
This is the point at which the scales tip, meaning the limitations of no cross
district trade are exhibited in the form of some districts suffering massive prices,
and others extremely low prices.
Wealth Distribution and Global Wealth
As may be expected, there is a clear correlation between the percentage of agents
unable to produce both goods, and the Gini Coefficient - a measure of wealth
inequality introduced in the previous chapter. This relationship can be seen in
Figure 4.8. As the percentage of agents able to produce both goods increases,
the distribution of wealth across all topologies becomes more even indicated by
the decrease in the Gini coefficient. The variation between topologies is still
virtually negligible.
In addition, the higher in wealth inequality actually reflects a far more re-
alistic world. In reality, the Gini coefficient for areas with respect to income
distribution such as the UK and the USA is approximately 0.35. Thus it is
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Figure 4.7: The effect of increasing the percentage of agents unable to produce
both goods on standard deviation
fairly realistic that in a free market, not so dissimilar to that of the UK, this
level of wealth inequality is realized. However as previously mentioned, wealth
inequality is thought to be quite a lot higher than income inequality so perhaps
there is still room for increasing the coefficient.
So what is causing society to become so much more unequal when the per-
centage of agents able to produce both goods is low? It can’t simply be the
unevenness imposed by not all agents being able to produce both goods, since
when no agent can produce both goods, the level of inequality is higher still.
Over time, as may be expected, global wealth falls as production capacity falls.
However, what is interesting is that the wealthiest agents remain relatively un-
affected, and the poor just get poorer (when the percentage of agents able to
produce both goods is low), thus widening the gap and increasing the Gini co-
efficient. However, the fact that the wealth of the wealthiest agents remains
unaffected, whilst global wealth actually falls implies that the rich are richer
relative to the other agents. This further reinforces the justification as to why
the distribution of wealth is more uneven when less agents can produce both
goods. Even though this explains the uneven wealth distribution, why the poor
become relatively poorer, and the rich relatively richer is still unexplained.
The rich in society are still pure producers. They also have an increasing
number of agents wishing to intiate trade with them. Thus they get more free
exchanges when the percentage of agents able to produce both goods is low. As
a result, the rich are becoming richer as their product is in demand. This is
analogous to the theory in economics known as wealth condensation. This states
that there is a correlation between being rich and earning more - new wealth
condenses to the already wealthy. In the context of the simulation, there is a
correlation between being proficient in the production of a good, and becoming
wealthier as a result. This is trivial to see, since if you can produce more, you
will be wealthier. However, what is less trivial, is how increasing trade affects
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Figure 4.8: The effect of increasing the percentage of agents unable to produce
both goods on wealth inequality
the distribution of wealth. Now, if you are proficient in production of a good,
you will become even wealthier than when there is less trade. This is due, as
mentioned, to the extra demand for goods since less agents are able to produce
both, more are forced to trade for it. This could be seen as unfair allocation of
resources, however, on the other hand, perhaps it is reasonable to expect that
in a free market, those who can do something well reap the rewards of their
ability. Perhaps it would be more unfair if they did not become wealthier for
providing a good service.
Figure 4.9: The effect of increasing the percentage of agents unable to produce
both goods on the wealth of the wealthiest agents
Now let us examine why the poor get poorer when less agents produce both
goods. Recall that for pure traders, trading was a last resort. Despite the
increase in trade, being a pure trader is still a last resort. Those who can
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rely on agents initiating trade with them become pure producers and enjoy the
wealthier life. Traders however, are those who rely on the pure producers for
trade. As discussed, new wealth condenses to the already wealthy, thus, this
wealth is not available for the pure traders. So how does wealth condense to
the already wealthy? Since pure traders are constantly surrendering goods in
trade to their trade partner - the pure producers, they are constantly increasing
the wealth of producers and simultaneously hindering the growth of their own
wealth. They simply survive.
Figure 4.10: The effect of increasing the percentage of agents able to produce
both goods on the wealth of the poorest agents
The graphs in Figures 4.9 and Figure 4.10 show wealth of the wealthiest and
poorest agents respectively against the percentage of agents able to produce both
goods. An interesting point on the graph depicting the wealth of the wealthiest
agents in the sharp decrease in wealth when the percentage of agents able to
produce both goods increases between 40% and 60%, for the local disconnected
network. Incidentally, this is the same range where the massive increase in
standard deviation occurs, so it seems that this is an important tipping point
in the local disconnected network.
So as the amount of trade increases, more dependencies emerge, and the
emergence of wealth condensation favours the rich and punishes the poor in an
increasingly divided world.
4.2.3 Conclusion
In conclusion, the increase in trade has highlighted how initial conditions affect
the evolution of the simulation. It has shown a progressive movement, redefining
profiles of the categorized agents as product specialization is imposed by the
system. We also witnessed a tendency for agents to become extreme specializers,
and even saw the percentage of pure producers increasing. The effect of a
local disconnected network on the dispersion of prices was further exaggerated
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with the increase in trade, and we saw the sensitivity of the local disconnected
network to the increase in percentage of agents unable to produce both goods.
The Gini coefficient better reflects reality, and indicates the divide in rich and
poor. However, people often suggest that wealth distribution follows the Pareto
Principle or 80-20 rule, thus although it is more realistic, it is difficult to judge
the difference between income and wealth distributions, even when dealing with
countries such as the UK.
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Chapter 5
Introducing Consumption
For Survival
Consumption is the act of consuming one of the goods. In the simulation, Good
2 is representative of money, which is not consumed. Good 1 encapsulates every
other conceivable good, which can be consumed. In the model, agents must now
consume a fixed quantity of goods, and if they are particularly wealthy, they
consume more. Being unable to consume the required, or baseline, quantity
reflects an agents inadequacy in the economy and forces an economic death,
which is to say, the agent exits the economy and hence the simulation. This
chapter focuses on the questions of why to consume, how it was achieved and
what the consequences were. It also looks at the threshold values for the baseline
amount to consume - what is a sustainable quantity?
5.1 Motivation
Consumption is inherent in society. It also ties in with the notions of wealth and
distribution. In essence, wealth can be a better indicator than income (strictly
in this context
1
) when it comes to testing how an agent in the economy can
perform when times are bad - does the agent have a stock of goods cushioning
it? Consumption in the context of the economic simulation is not akin to the
consumption of food and so on, it is more reflective of expenditures to sustain
their “business” of production and trade. Importantly this is not necessarily a
monetary cost, but rather it is the resources needed - machines, ingredients and
so on - so costs are not reflective of money - Good 2 - but it may be necessary
to spend Good 2 in order to acquire resources - Good 1.
1
Its suitability in this context stems from the fact that there are no liabilities - no debt.
In the real world, measures of household wealth often class people in the west as poor since
they have more debts than assets! Thus, in reality either a notion of income is used if you
are studying it on a household level, or a combination, or wealth if you are investigating how
good a country’s finance sector is etc.
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There are several pertinent questions to be addressed at this point. Firstly,
why do the wealthier consume more? A poor performing agent in the economy,
who is able to produce little of either good, for instance, is analogous to a small
business. Its size is reflective of costs, and a small size has lower total costs.
Similarly, someone who is particularly wealthy and is extremely proficient in
production of some goods is a bigger player in the economy, and thus has higher
costs. For example, the cost of running the factories of a massive food producing
company supplying to supermarkets are far greater than that of a local farmer
growing small amounts of produce to sell This explanation deals with producers,
but what about the traders? The traders act in a similar fashion. Less wealthy
traders often trade in smaller quantities, and bigger traders in large quantities.
The cost of standing on a market stall selling the produce of the local farmer is
far less than that of shipping the immense quantity of ingredients from a huge
farm to the massive food producing factory for them to make their products.
We might then consider how one can need Good 1 to produce Good 1? Since
Good 1 encompasses all other goods, it is a very abstract notion of a good. In
the simulation we cannot distinguish between Good 1 being an apple and Good
1 being a lorry, nor is it necessary to do so. All that need be represented is that
production and trade are not free, stocks of goods do not increase infinitely and
prices are affected by the level of demand. So we can introduce consumption -
the exiting of goods from the economy through use -as a new way of finding the
agents who can sustain themselves in this world, and a new sort of demand for
goods.
Consumption - or resources needed by businesses - is extremely relevant,
especially in today’s economic environment. Examples of the importance of
sustainability of consumption by businesses, and their dependence on price fluc-
tuations and changing levels of demand are in abundance. The most obvious
example for price rises is the effect of the rises of oil price on virtually all busi-
nesses. Oil underwent huge price increases in the years of 2003 to 2008 - its
price per barrel increased approximately by a factor of 4 [11]. Contributors to
these price rises are increased demand: as developing economies develop they
tend to consume more resources that relate to wealth (for instance oil for cars)
and that drive economic growth. This, coupled with the slowdown of petroleum
production and other oil-related products means that the difference between
supply and demand is furthered and prices increase. The increases affect all
businesses using transport - distribution companies, the shipping companies,
air travel companies and even restaurants. This is indicative of both the size
and scope of the effect that changes in supply, demand and prices of goods have
on companies. In this simulation, consumption introduces the notion of scarce
resources and looks at the effect it has on the dynamics of the simulation.
5.2 Implementation
A key necessity was for consumption, in the beginning, to be feasible for the
large majority of the population. Therefore, the baseline quantity - the necessary
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amount to consume was computed at the beginning of the simulation.
In the simulation, the baseline quantity was set to be a proportion of the
average stock of goods existing as initial endowments in the world. Mathemat-
ically:
C = a ×
(∑
n
1
(g
i
1
+ g
i
2
)
2n
)
where
C is baseline consumption, a some constant less than 1, n is the total num-
ber of agents, g
i
1
, g
i
2
are the stock of Good 1 and Good 2 that agent i is endowed
with respectively.
This baseline was the amount of Good 1 agents had to consume on every
mathematics iteration. It was necessary to vary a and n in order to find stable
values for both of them, so that some agents were still affluent, some agents
were poorer, and agents could (for the most part) still exist in the economy
for prolonged periods while simulataneously having consumption influence the
simulation in some way.
The extra amount an agent is to consume is set to be a proportion of their
current stock of Good 1:
E = b × (g
i
1
+ (
g
i
2
p
))
where
E is the extra amount of Good 1 to consume, b is a constant less than 1, g
i
1
, g
i
2
are the current stock of Good 1 and Good 2 respectively held by agent i and p
is the average price of Good 1 at the point in time.
Let us go on in the sections that follow to look at the effect of changing these
variables, a and m, on the evolution of the simulation, to find stable points and
to use these points to evaluate the new world with consumption.
5.3 Evaluation
5.3.1 Evaluating values for constants
In order to implement consumption and ensure a balance between a stable sim-
ulation and being able to see the effect it had on the evolution of the simulation
it was necessary to perform experiments to attempt to find stable points. There
is in fact a fine line between a chaotic simulation riddled with bankruptcy and a
stable simulation with little effect on anything but wealth. The effect on wealth
is easily explained by the fact that consumption means goods leaving the system
and thus the total stock of Good 1 will definitely be reduced, and stock piles
will not grow infinitely thus wealth is considerably lower.
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In order to find a stable point, two things were varied: the value of the con-
stant a used in calculating the baseline amount to consume, and the frequency
of consumption, m - agents had to consume every m iterations. The value of a
was set to be 0.03, 0.06, 0.09 and m was set at 1, 3, 5. Every permutation of the
following was tested. Each simulation ran for 2000 iterations, with 20 districts,
20 agents per district, 2 crossover agents (if applicable) and 20% of the agents
able to produce both goods. Simulations were run for the Local Connected,
Disconnected and Small World Networks. Results for each were averaged over
10 simulations. The values for the baseline quantity to consume are given in
Table 5.1 with the corresponding a value.
a
Baseline
0.03
1
0.06
2
0.09
3
Table 5.1: Table showing value for a and corresponding baseline to consume
Four areas were examined in order to evaluate the effect of the values that m
and a had on the evolution of the simulation, namely, the level of trade, average
wealth, wealth distribution and price. In addition, significance testing indicated
that the differences across topologies were insignificant and thus the topologies
will not be examined in isolation.
The results revealed that the largest contributor to the evolution and stabil-
ity of the simulation was the value chosen for m. The amount of time between
agents having to consume consistently resulted in dramatic differences in the
ability of agents to cope with the requirement of consumption.
Beginning with m being set to one, agents were forced to consume on every
iteration. In this way, agents who are unable to save up Good 1 over a period
of time end up suffering massively, and those who suffer the most are the pure
traders. They are typically unable to produce much of either goods, and as
such are forced to purchase the quantity they are to consume. Due to their
poor production proficiency in both Good 1 and Good 2, and the fact that they
are required to consume on every iteration, they were the first to go bankrupt.
Surely however, they would be able to purchase the goods from agents who
are most proficient in production. Unfortunately, agents who are proficient in
the production of Good 1 consume more, and are unrealistically less wealthy as
a result. A lot of trading opportunities evaporate for the pure traders. Their
stock of Good 1 and Good 2 is low, and pure producers have a larger amount of
Good 2 than Good 1 - Good 2 is not exiting the system. This large difference
can be seen by inspecting the movement of goods for a pure producer illustrated
in Figure 5.1. The stock of Good 1 stays relatively constant, and low, whilst
the stock of Good 2 grows. Thus, since price between two agents is calculated
to be
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Figure 5.1: Illustration of skewed stock piles, even for a pure producers causing
price inflation
P
i,j
=
g
2
i
+ g
2
j
g
1
i
+ g
1
j
the price for one unit of Good 1 is extremely high if the quantity held of Good
2 is far greater than the quantity Good 1. To see just how large fluctuations
in price are, and to see in addition how high they are (considering without
consumption they approximate to 1), see Figure 5.2. This in turn means that
pure traders who can’t produce Good 1, and can produce only a small amount
of Good 2 are unable to afford just one unit of Good 1 hence are bankrupted.
This forces the level of trade down significantly for this value of m, as illustrated
in Figure 5.3.
The level of trade falls below 1% for m = 1 and a > 0.06 as pure traders are
bankrupted and trading ceases. Pure traders being bankrupted however is not
the only reason for this massive decline in trade. In fact, there is also a change
in strategy of agents. Pure traders who can produce the required amount of
Good 1 migrate to the pure producer category. This can be seen by comparing
the two specialisation graphs, mapping the production ability of an agent with
their specialisation shown in Figure 5.9. On the x and y axis we have how much
they can produce of Good 1 and 2 respecitively.
Each series corresponds to a specialisation category. With consumption
(Figure 5.4a), pure producers emerge when production of Good 1 is lower and
Good 2 is 0. They can survive by producing then consuming. Pure traders
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Figure 5.2: Illustration of how skewed stock piles effects prices
are only apparent when they can produce 0 or practically 0 of both Goods.
In addition, with consumption heavy producers now occupy the region where
Good 2 is produced and Good 1 isn’t, or the amount is small. This shows that
those agents who used to be pure producers (shown in Figure 5.4b) are now
forced to engage in more trade in order to allow them to consume - a strategy
shift. Far less agents are in a position to initiate a sale of Good 1 so they can no
longer rely on agents initiating exchange with them. These dramatic strategy
shifts indicate the new demands that have been inflicted on the popualtion have
radically changed the dynamics of micro interactions between agents.
As a result of the miniscule amount of trade, prices seem uneffected by the
value of both a and m. However, this is misleading since prices are rarely made
thus they seem not to be inflated relative to the other values for m as seen
in Figure 5.5. Wealth however, is a very good indicator of how devastating
frequent consumption is on these agents. Average wealth falls dramatically to
under 1000 units when consumption on every iteration is required. This can be
seen in Figure 5.6. By simply increasing m to 3, average wealth is increased by
a minimum of 6 times. In addition, when m is at 1, the Gini coefficient is at its
lowest - not because society is more equal, rather, the poor exit the economy
(Figure 5.7).
The difficulty caused for agents when faced with such frequent consumption
also means that the effect of the value of a is negligible. However, when m is set
to 3, agents have time to save, and trade is increased ten fold for a low value of
a. At this value for m, changing the baseline quantity to consume has a greater
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Figure 5.3: Level of trade as m and a are varied
effect. Trade falls sharply as a is increased from 0.03 to 0.09. Two things are
occurring here. Firstly, some pure traders are unable to consume this amount,
as they can neither produce it, nor afford to buy it. By inspecting the graph
in Figure 5.5, it is apparent just how difficult it is for agents unable to produce
enough Good 1 to purchase it instead. The average price has risen to over 20
times the price relative to without consumption. As Good 1 exits the system,
we witness inflation - the demand for Good 1 is increased and in addition the
supply is restricted. Secondly, some pure traders can produce enough to sustain
their livelihood, and as such turn into pure producers.
In addition, wealth falls substantiall as a is varied when m is at 3 (Figure
5.6). This value for m is the value at which the baseline amount to consume has
the greatest effect. Consumption is manageable, but fragile - it depends heavily
on how much agents are expected to consume. An interesting point for when
agents are to consume every third iteration is the effect that varying a has on
price (Figure 5.5). For other values of a, price is unaffected, however, now it
is reduced by half between a being 0.03 and 0.09. What causes prices to fall
is fairly misleading. As more agents are bankrupted or move to become heavy
producers, indicated by the fall sharp fall in trade, demand for purchasing Good
1 is greatly reduced. There is the more Good 1 available to a smaller population
and thus it falls. Imagine at a being 0.03, many agents are competing for Good
1. As such, the stock piles of those agents with a good ability in the production
of Good 1 is fairly low as so many agents are buying it from them, which pushes
up prices. However, as the price starts much higher when a is 0.09, thus a lot
of agents can never afford to buy it and exit the economy, removing a large
proportion of the demand. This means supply is less scarce, and producers
make less sales. As a result, their stock piles of goods become marginally more
even - enough for prices to fall over the long term.
Moving m to 5, the effect a has is dampened. Trade still falls, but both
less sharply and to a higher value. Wealth is far greater and doesn’t change
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(a) With Consumption
(b) Without Consumption
Figure 5.4: Correlation between specialisation and production functions
significantly. It is important to note, that since wealth accounts for price, and
the price is lower when m is 5 relative to when m is 3, the increase in wealth
when m is 5 is actually of even larger significance since average wealth is higher
despite the value of Good 1 being lower.
In additon, the Gini coefficient is higher when m is 5 (Figure 5.7). Despite
the difference being small when m is changed from 3 to 5, the negligible variation
proved this to be significant via a means test. The reason for the heightened
uneven wealth distribution is that their are fewer bakruptcies and so the more
poor agents can survive the harsh world. As a is increased, the Gini coefficient
decreases slightly as less agents survive.
Another interesting point on wealth is that the growth or creation of wealth
in society has a different trend. Without consumption, recall the increase of
wealth over time presented a linear trend (although fluctuating with price move-
ments). However, when consumption the frequency and baseline are low enough,
this now becomes more logarithmic. This is illustrated in Figure 5.9b. We have
wealth creation, however the rate of growth is slower and more realistic. On
the other hand, move consumption to be carried out on every iteration and
a dramatic change occurs: wealth creation ceases (Figure 5.9a). There is a
sharp increase at the same time as a major spike in prices (Figure 5.8), and
then wealth remains constant for the entire duration of the simulation. At this
point, the new wealth created on every iteration of the simulation is either im-
mediatey consumed or exits as an agent becomes insolvent. This is consistent
for all values of a when m is set to 1. This is illustrative of the importance of
initial conditions on the evolution of complex dynamic systems.
In conclusion, it is clear that consuming on every iteration when a large
proportion of the population are unable to produce both goods is not sustainable
and prevents economic growth. It seems the best value is for agents to consume
as little as possible as infrequently as often - setting m to 5 and a to 0.03. This
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Figure 5.5: Level of trade as m and a are varied
Figure 5.6: Level of trade as m and a are varied
way less deaths occur and the less fortunate agents have a better chance of
avoiding bankruptcy. However, one problem is that the wealthy agents perhaps
consume too much - leaving supply to dwindle and poorer agents to suffer. In
the next section, the additional quantity for the wealthy to consume will be
reduced to the same value as a.
With respect to how realistic it is, the answer is, not very! The poor have
little opportunity. Perhaps though this is not a downside on actual consumption
in the model, but the limitations of not allowing borrowing or financial support
for the poor. With banks, pure traders would be able to make massive margins
through riding the price fluctuations, however the capital just isn’t there for
them to begin with. Thus, perhaps introducing an additional interaction of
borrowing could allow for traders to engage in trade and exploit the prices - an
interesting extension.
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Figure 5.7: Gini Coefficient as m and a are varied
However, the importance of initial conditions was reflected in the changes
of straegies witnessed and the price inflation was indicative of the importance
of balance between supply and demand. The Gini coefficient was increased as
more agents were living on the bare minimum, and less bankruptcies occurred.
This can be viewed as analogous to the distribution of wealth of companies: an
economy where more firms can survive in a market place irrespective of their size
- in other words it is less monopolistic. Although the difference in importance
and wealth varies drastically, the fact that small industries are permitted is
realistic.
5.3.2 Bankruptcy Chains
Throughout the report an emphasis on the important of networks - the interac-
tions between agents - and their applicability in economics has been suggested
but not addressed. In this section, consumption is used to examine the appli-
cability of network theory to the study of bankruptcy chains. A bankruptcy
chain in this simulation constitutes the bankruptcy of one agent facilitating the
bankruptcy of others which in turn can cause more. It can be thought of as a
domino effect. Here, an investigation into predicting whether the dependencies
of agents on a bankrupted agent would cause the dependents to also go bankrupt
is conducted and compared to the results of the simulation in order to evaluate
its usefullness and accuracy. In addition, the applicability of this idea to the
field of economics is assessed.
A problem with this investigation is that often, agents are dependent on
pure producers, who more often than not survive. Thus bankruptcy is forced
upon a single pure pruoducer, and the effect of this on other agents in the
population is examined. The pure producer to be bankrupted was chosen based
on a heuristic: when consumption is employed the best trade partners are those
who can produce alot of Good 1 and little Good 2. Thus an agent fitting this
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Figure 5.8: Prices for m = 1, a = 0.03
description is searched for, and the first one encountered bankrupted (removed
from the simulation). Deaths and trades are recorded before and after this event
to facilitate examination of changes in network structure and resilience for two
topologies, the local disconnected and small world networks.
Iterestingly, both realisms and fundamental flaws in the model at hand be-
came apparent upon conducting this investigation. First, the performance of the
heuristic will be assessed prior to discussing the results of forced bankruptcy on
the local disconnected network and the small world network; finally a discussion
on what is severely lacking will follow.
The heuristic is to bankrupt a producer with a high proficiency in producing
Good 1 and a poor proficiency in producing Good 2. In order to assess the
success of the heuristic, it is necessary to define the aim: to bankrupt an agent
who many agents would want to initiate trade with. In order to measure the
success of this, a notion of network centrality was employed, specifically degree
centrality. This measure bases its calculation on the assumption that an impor-
tant node in network is one which is connected to many other nodes. In the
context of the simulation, this is precisely what we are looking for. A matrix of
agents in a district is constructed, with every agent labelling a column and row
- so for a district of 20 agents a 20 by 20 matrix is constructed. Each position
i,j in the matrix represents the percentage of all Good 1 bought by agent i that
came directly from agent j. The average percentage is calculated across the
whole district and this value is taken to be a threshold representing meaningful
purchasing. Each agent in the district is represented as a node in a nework.
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(a) With m = 1
(b) With m = 5
Figure 5.9: Gloabl Wealth varying m
For each meaningful purchase by agent i from agent j, an arc is added between
them travelling from node i to node j. Since this represents purchasing Good 1,
it is indicative of a dependence agent i has on agent j to remain solvent. Thus
this network can be seen as a network of dependencies. The degree centrality
for node j is then calculated to be:
C
D
(n
j
) =
d(n
j
)
N − 1
,
where C
D
(n
j
) is the degree centrality for node j representing agent j, d(n
j
)
is the number of edges leaving node j and N is the total number of nodes in
the network [14].
For all 20 simulations conducted, 80% of the time, this heuristic resulted in
the node with the highest degree centrality being subjected to forced bankruptcy
and 20% of the time the node with the second highest. Thus the heuristic based
method for selecting victimes was successful.
Local Disconnected Network
In the local disconnected network, the fact that each district is isolated from
the rest of society means that any implications resulting from forced bakruptcy
are self contained within the district that the victim lives. Thus in order to
investigate the effect, it is necessary only to examine the victims district.
All the results from the different runs were fairly similar hence for clarity
only one will be focussed on. Figure 5.10 illustrates the network produced prior
to the forced bankruptcy. The victim agent is agent number 303. As you can
see by inspecting this node (red) this has the most inbound edges out of all
nodes in the network.
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Figure 5.10: Illustration of trade network, victim in red, children in pink, parents
in grey
Each child in the network is coloured in pink. These are nodes who only
have outbound networks - noone is dependent on them. The grey nodes are
dependent on noone. As shown, there are no nodes who have both inbound
and outbound nodes. This actually presents a large flaw in the model. It is
indicative of the fact that traders depend on only producers, producers depend
on themselves, and nobody depends upon traders. As a result, upon analysing
bankruptcy chains, bankrupting the victim can only ever have an affect on
anything directly dependent or transitively dependent on them. Since transitive
dependence doesn’t exist, it can only ever affect the nodes siblings. This lack
of transitive dependencies brings to light an big flaw of the model. It shows
that traders are not only poorest and most vulnerable to supply shortages, but
also that they, never make enough profit to sell on a good they buy and this
prohibts trade chains. They trade only for survival - they do not make large
margins and they cannot exploit their position to do so. The simulation does
not value traders.
As a result, despite the forced bankruptcy being damaging to the direct
buyers, the damage stops their. This is massively unrealistic. Take the current
recession to be an example. An initial mistake in the financial sector, specifically
“mortgage backed securites” (asset backed securities where cash flow is backed
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by a collection of mortgage repayments) caused the bust of the housing market.
This in turn caused home depot stores to suffer, as well as building industries.
Banks suffered huge losses and grew cautious of lending money, meaning in-
vestment was hampered through lack of getting a loan. This has a knock on
effect in economic growth, unemployment has risen and much more. The point
being that despite the simplicity of the model economy being used, you would
expect some domino effect. As it is, we have a single bankruptcy effecting only
its children simply due to the fact that these children have no children of their
own. The path length for goods moving from one agent to the next is too short.
This is due to the fact that noone, not even pure traders themselves, wish to
buy from other traders. This results in having a network in which there are a
few centers of gravity - nodes who have lot of dependents and are important in
the network. These attractors in the network are rarely connected to each other,
nor are their children connected to other children. There are simply nodes who
have children and these children have multiple dependencies.
However, despite the “chains” having a depth of one, the victim’s bankruptcy
did have an effect on some of its dependents 100% of the time, and also on others
who suffered from the change in the network structure. Hence we shall move on
to discuss exactly what was observed upon this occurring.
Figure 5.11: Illustration of trade network after bankruptcy of victim
Figure 5.11 shows the network that was formed after the bankruptcy of our
central agent. The dark coloured nodes are agents who were both dependent
on the victim, and were bankrupted some time after his bankruptcy. The blue
node reflects an agent who was dependent on the victim, however, survived his
bankruptcy. The peach node reflects an agent who was not dependent on the
victim, but became insolvent after the victim. All other nodes survived and
had no dependencies on the victim and they are either parent nodes (grey) or
children (beige). Finally, edges drawn in blue are new, and edges drawn in black
existed prior to the bankruptcy of the victim. For clarity, a key is provided in
Table 5.2.
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Shade
Meaning
Dark
Agent bankrupted, was dependent on victim
Blue
Agent survived, was dependent on victim
Peach
Agent bankrupted, was dependent on victim
Other
Agent survived, not dependent on victim
Table 5.2: Key for the colour coding of the networks
Firstly it is important to notice that the overall structure of the network
changed dramatically in response to the removal of the victim. His dependents
found new suppliers of Good 1, as illustrated by the many blue outbound arcs
from the dependents in the diagram. Also notice, that the all the bankruptcies
are on the agents who depend heavily on just 6 other agents. For clarity, this
portion of the network is separated and shown in Figure ??. Further, this figure
shows agents who, prior to the bankruptcy were dependents themselves, or not
dependent on anyone with noone dependent on them. They were the agents
less good for intiating trade with and as such were self sufficient. However,
on removal of the central node, these agents have a chance to become wealthy
through new demand for their products. However, evidently they were unable to
supply the quantity needed at reasonable price to all those agents who had been
dependent on the victim. As such, the network has become overloaded. Even
an agent who was not dependent directly on the bankrupted agent falls victim
to the supply shortages and price inflation caused by this change in structure.
It is clear that the model allows for agents to build new connections, interact
with new agents when faced with this sort of economic crisis. However, in spite
of this, they are still unable to survive and the reasons as to why are really
quite simple. These new arcs, or dependencies that form were not apparent at
meaningful levels of purchasing previously for a very good reason. They were not
as good as the victims prices, they could not offer the victims quantities to all
the agents. In essence, a new network structure forms with new dependencies,
but these are not sustainable relationships. These nodes cannot cope with this
new load and can’t serve all the agents at the prices they need. As their stock
pile of Good 1 is depleted, prices soar, and as a result become unaffordable to
many. This explains why it is plausible that this extra load actually indirectly
effects (not through a chain as such but through supply shortage and inflation)
an agent who was in no way dependent upon the victim.
What is extremely interesting is those who do not succombe to bankruptcy
and survive, even purchasing as high a quantity of Good 1, for the duration of
the simulation. Again, for clarity, a separate illustration can be seen in Figure
5.13. Now, the brown node wasn’t dependent on the victim in the first place,
however he is heavily integrated in to the overloaded network. There is however
a massive difference. He is in addtion dependent on a node outside of these
Good 1 providing hubs. He is also a suitable trade partner for an agent with
one two dependents. Two dependents is surely far more sustainable than six!
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Figure 5.12: Illustration of common dependency
The blue node illustrates this point further. Previously dependent on our victim,
he then forms an entirely different network virtually completely disjoint from
the overloaded one. These agents provide only to him, and as such he is able to
avoid bankruptcy through sourcing his Good 1 from an isolated set of agents,
resulting in a reliable and sustainable network with redundancy in the case that
one of the nodes he is dependent on suffers high prices or supply shortages.
Figure 5.13: Illustration of survivors
We have seen that although the path lengths in the network prohibit the
notion of bankruptcy chains effecting more that one person, the bankrupting
of the central agent does have an impact on the ability of dependent agents to
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survive. We also saw that a change in network structure causes knock on effect
to agents who weren’t dependent on the bankrupted agent. It seems that de-
pendency cannot capture, but can illustrate, the potential economic difficulties
caused by removing an important node. In addition, it has revealed that hubs,
or agents with high degree, are a source of vulnerability for its dependents when
the dependent only engages in trade with other hubs. Low centrality means
resources aren’t stretched as far. It is evidently important to be dependent on
not only central hubs, but also on nodes with low centrality. This avoids compe-
tition from other agents, and this competition contributes to supply shortages
and price rises.
5.3.3 Conclusion
In order to anticipate the agents which will be bankrupted after, it is necessary
to consider both the network prior to and after the the victim has been forced
out of the economy. The agents likely to be bankrupted are those who were
meaningfully dependent on the victim and who are attracted to the same set of
agents, which become hubs as the network restructures. If these agents weren’t
previously hubs, or had considerably lower centrality, it is likely that the new
load will not be coped with. In this situation all agents dependent on hubs and
only hubs will be bankrupted. In the simulations studied, 75% of the time the
hubs that emerged after the bankruptcy had previously had no inbound edges.
However, after the bankruptcy, they had the highest centrality in the network.
This shift illustrates the fact that previously these had not been the best trade
partners and hence it is unsurprising that they could not cope with the new
load. In addition, 75% of the time, the new hubs were actually agents who
both had no dependents and depended on noone prior to the victim exiting the
economy. This shows they were able to produce enough Good 1 to sustain them
selves, but their stock piles didn’t suit those in need of Good 1 as well as the
victim.
This dependency network was useful in analysing the disruption caused by
the most central agent exiting the network. The way in which there were hubs
and these hubs were not linked to each other shows the network was composed in
a similar manner to the star network - in which there is one central node which
all nodes must go to. The network seen differed in that there were multiple
hubs or stars, however the lack of transitivity, cycles and so on made for a
fairly inefficient network, which is likely to contribute to the poor resilience of
the dependents on the victim. To formalise as opposed to speculate the low
efficiency on the network structure, and the vulnerability of the network to
removal of a victim, the network efficiency can be computed as:
E(G) =
∑
n
i=1
∑
N
i>j
1
d
ij
N − 1
where E is the efficiency, G is the graph, N is the number of nodes, and
d
i
j is the distance between node i and node j. If j is not reachable from i, the
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distance is undefined [14].
The average efficiency in the local disconnected network was 0.152 prior to
the bankruptcy. The expected change in efficiency, or a measure of vulerability
stemming from the deactivation of the victim v can be computed as:
C
I
v
=
∆E
E
=
E(G) − E(G )
E(G)
where G’ is the network attained through removing the edges and node of
the victim [14].
The average efficiency of the initial trade network was calculated to be 0.152
(values range between 0 and 1, 1 being the most efficient). After removing the
victim node, the new efficiency was calculated to have fallen by 39%. When
comparing this fall in efficiency to the actual computed efficiency of the new
network that formed, it differed by only 3% on average. Thus despite the new
formation of nodes, and the different nodes coming in to the equation, the
formula was extremely accurate.
This fall in efficiency by over one third is indicative of the fragility of the
network caused by such hubs and the short path lengths. Although it can
recover structurally, unfortunately this isn’t sustainable. In order to determine
just how star like this is and thus how expected the bankruptcies are due to
network structure, the trade network was compared to that of a star network of
equal size. A star networks vulnerability comes from the single point of failure.
The central node or hub is the only means of communication, or in this case,
the only means of Good 1 reaching the other nodes or dependent agents. If
the network formed is similar to that of a star structurally, it is reasonable to
anticipate the catastrophic effect of forced bankruptcy on dependents, and thus
can begin to analyse precisely why this structure amongst agents occurs. If
however, it is not the case, then the contributing factor is not to do with a
problem of network structure.
The similarity of the structure to that of a star network can be calculated
as:
C =
∑
g
i=1
(
C
d
max
− C
D
(n
i
)
)
(g − 1)(g − 2)
where C is the centralisation index, C
d
max
represent the actual maximum
degree observed, and g is the number of nodes.
In fact, this indicator reveals that the network as a whole is fairly decen-
tralised, with a centralisation index of on average 0.3 prior and 0.16 after the
bankruptcy of the victim. This not only shows low centralisation to begin with,
but in addition, it becomes more decentralised after the readjustment. This is
in comparison to one in which a victim isn’t chosen, where centralisation re-
mains consistent throughout the simulation. The decrease in centralisation is
perhaps quite telling of the struggles the agents face. Decentralisation occurs
when more nodes are connected to other nodes - or there are more centers of
gravity. However, this is indicative of the fact that a more centralised network
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is no longer possible after the bankruptcy. Agents used to be able to rely on
a few select sources, however, removal of the important node forces agents to
acquire goods from more sources, making the network more decentralised.
There is another problem in the results of this investigation which provides
insight into the limitations of the model employed. The maximum path length in
the trade network for a district is consistently one when conumption is enabled.
There is no need for agents to buy from anywhere other than the producer.
Thus no value is added in the traders purchasing a stock of goods as they have
to initiate the next sale and no one buys it from them. Traders lose out when
consumption is enabled since nobody depends on them. This is because if you
need to purchase something from a trader, it is highly probable that you will
receive both a better price and quantity from the producer directly. Since you
have access to the producer, you will go there. In reality, abstractly, value is
created when goods are moved from one location to another. The reason for the
value being added can be anything from scarcity of the product where they are
moved to, to the fact they are converted to a good which has more demand and
thus higher value. For a more intuitive example, think about chocolate. Cocoa
beans sourced from Africa are bought for an extremely low price from third
world farmers. When they are sold to Cadbury’s, a massive margin is made.
Cadbury in turn makes its chocolate bars and sells these to Tesco for far more
than the ingredients cost to purchase. Tesco sells these to consumers, again with
a large mark up. The model however, doesn’t reward traders well enough for
this value creation, or in anyway at all. They buy cheap in one round and sell
dear in the next, however, the fact that they are poor means not a lot gets moved
and thus only a small margin is made unlike the producers who experience free
exchange. In addition, their poverty increases what they charge and thus are
never a valuable trade partner. This in turn means producers won’t seek out
traders as they can rely on traders seeking out them. This means that long
trade chains aren’t witnessed as everybody in need of purchasing a good can
go straight to the producers. There are no middle men involved in the process.
In reality, long trade chains exist, with each sale creating more value as a good
is moved from one place to the next. In addtion, in the real world traders
are not poor. On the contrary, merchants’ knowledge of the trade networks
they were involved in allowed exploitation of prices and they were some of the
wealthiest. Even today, shipping companies make vast amounts of money - far
more than the third world farmers. It is likely that the maximum trade length is
a limitation. With consumption, the possibility of traders selling Good 1 is slim
due to the poor prices they offer and the fact that they need it to survive. This
topic is to be discussed in the final conclusion where suggestions for enhancing
the model will be presented.
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Chapter 6
Permitting Agents to
Remember Encounters
So far, agents search through their district in order to determine who the best
trade partner is. We saw in Chapter 3 the effect of restricting the number
of agents that an agent is permitted to search through in order to find a trade
partner. Now we ask, what happens if the number of people an agent can search
through is restricted, but they can also choose to store those agents with whom
they had an exchange, and search through agents in their memory in each
round? For memory to be applicable or useful to agents, in the simulations
used in evaluation trade is increased by raising the percentage of agents who
can produce only one good to 20%.
An investigation into the usefulness of memory and also the effect it has on
the number of distinct trade partners an agent has and the long term trading
relationships that may emerge as a result is conducted. In addition, the effect of
memory size is assessed to help determine the importance of memory to agents.
Implementation of memory is analogous to sustained trading relationships. It
is a way of agents being able to learn who is a reliable source of a specific good,
and keep returning to that agent.
6.1 Motivation
The motivation behind remembering trade partners is twofold. Firstly, it is
more realistic that an agent strategically records those who are suitable trade
partners for them. In reality, we do not randomly select where we will buy
our shopping, but we know from experience where the best places to go are.
We know the corner shop is overpriced from having to pay 3 for tinfoil, and
so only go there when we have no choice. We know that Tesco is quite cheap
from having bought Tesco Value baked beans at 9p, but that, at the moment,
if we want sausages, Sainsbury’s has a discount. Although more factors than
price come into it in the real world, and this is a massively simplified version of
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reality, the point is that we learn from experience where to shop. If an agent
knows that he always trades with a few select partners, why not be sure of
engaging in hypothetical trade with them in every round? Likewise, why waste
time searching through contacts with whom he has never engaged in trade?
Of course, agents will still use contacts, but a larger share of their potential
partners will come from memory.
The second motivation for implementing memory was the introduction of
learning, which is the topic of the next chapter. For this extension agents
had to be able to remember agents that they learn about and hence it seemed
important to also look in to the effect of memory in isolation from learning.
6.2 Implementation
In this section the logic involved in an agent making a decision as to whether or
not to store (if it isn’t stored already) an agent with whom he has engaged in
trade will be covered. It is also necessary, since agents do not have a memory
of infinite size, to explain the logic of deciding whom to replace in the memory
in the case of an agent wanting to store a contact and his memory being full.
There are, therefore, two decisions:
1. Should this contact be stored?
2. If the agents memory is full, who should be replaced?
It may seem initially that the first decision is easy: if there is space, store
the contact. However, it is not that simple. Since the majority of an agents
potential trade partners will now come from its memory, and anticipating the
implementation of learning, this means that you can’t store just any contact. It
is feasible to only have one exceptional contact who facilitates massive increases
in utility among the ten contacts in an agents list of potential partners, meaning
that even when an agent has free space in his memory, it is not desirable to add
everybody with whom he is engaged in trade.
Let us consider what determines why one agent would want to store another.
Firstly, it is relative in the sense that an agent is comparing the potential re-
membered agent to those who are already in his memory. Having considered
what constitutes a worthwhile interaction, it seems that the following two points
influence the decision.
1. Change in utility that the trade gave you
2. The MRS of the agent to be stored
While one might consider that change in utility and MRS will show the same
thing so perhaps one could be used over the other? The problem is that the
MRS of an agent captures the ratio of goods it owns in other words, how skewed
its stockpiles are. By comparing the MRSes of two agents, their suitability -
how well their stockpiles complement each other in trade becomes apparent.
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Should one agent have an abundance of Good 1, and only a small amount of
Good 2, while another has an abundance of Good 2 and only a small amount
of Good 1, They would be suited since the one needs Good 1 to balance out his
stocks, and the other needs Good 2. They could cooperate in trade so they both
benefit from balancing out their stockpiles of goods. However, MRS does not
capture the magnitude of the trade - the quantity exchanged. Utility, however,
does. The change in utility shows how close the ones stock of Good 1 is to the
others stock of Good 2 relative to the price. This is because if their MRS’s were
different, but the one was far less wealthy in how much of Good 2 he possessed,
the other may not be able to sell him as much Good 1 as he would like. Thus,
the change in utility indicates the quantity exchanged, which is an important
factor in suitability.
Now that the contributors are known, it is possible to decide whether an
agent is worth storing. Since, as mentioned, an agents value must be considered
relative to the value of the agents already stored, we can assign each agent in
memory a value reflecting its usefulness based on the two attributes, change in
utility and MRS relative to the other agents in the memory. However, we have
a twist in that both attributes must be taken into consideration. To do this,
I adopted a notion from Decision Analysis that allows a value to be assigned
reflecting the aggregate benefit of something relative to others. This aggregate
benefit is a value, between 0 and 1 in this case, that encapsulates the value of
every attribute to be considered. The steps taken are outlined below.
1. Calculate the aggregate benefit value of the agent to be considered to
store, call this v
p
2. Calculate the aggregate benefit value of each agent in your memory, using
the best trade as the trade for change in utility, call this set R
v
3. Compare v
p
to each element r
v
in the set R
v
:
(a) If there is an r
v
< v
p
and there is space in memory, store the new
contact
(b) If there is no r
v
< v
p
, do not store the contact
(c) If there is an r
v
< v
p
, and there is no available space, decide who to
swap
Now we just need to see how an aggregate benefit value is arrived at. Let
a
d
be the agent making the decision, a
p
is the potential agent being stored, and
a
i
r
is any remembered agent in the set of memory items, R
a
. The idea is that a
bigger change in utility gives a bigger value for utility, and a bigger difference in
MRSes leads to a higher value for MRS. The values are then equally weighted
(since their importances are equal) - they both carry a weight of one half. The
values are multiplied by their weights and summed to find the aggregate benefit
value. Formally they are computed as follows:
1. Find the range of changes in utility for all a
i
r
∈ R
a
, and a
p
. Let the
minimum change in utility be u
m
, and the range be u
r
.
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2. Find the range of absolute differences in MRS:
abs(a
d
− a
i
) ∀i ∈ R
a
, a
p
. Let the minimum difference be m
m
and the range be m
r
3. For all a
i
r
in R
a
, and a
p
, compute the value corresponding to their change
in utility to be:
u
i
v
=
u
i
− u
m
u
r
where
u
i
is the change in utility generated for agent i, and u
i
v
is the corresponding
value for that change in utility
4. For all a
i
r
in R
a
, and a
p
, compute the value corresponding to their differ-
ence in MRS from a
d
to be:
m
i
v
=
m
i
− m
m
m
r
where
m
i
is the difference in MRS between a
i
and a
d
, and m
i
v
is the corresponding
value for that difference in MRS
5. For all a
i
r
in R
a
, and a
p
, the aggregate benefit value for agent i, A
i
is
computed to be:
A
i
=
u
i
v
+ m
i
v
2
Now that the question of when to store has been answered, let us now tackle
what happens if an agent decides to replace an agent in its memory in favour
of a new one. How should who goes be computed? The method above could
be used, but comparing agents in memory that you have already had exchanges
with is more complicated. Issues arising include questions such as, how often
are they used? How long ago was it that you had your best exchange? How does
your most recent exchange compare with your best? In light of these questions,
I decided to use the same technique of aggregate benefit value only this time
with more attributes. You assign each agent in your memory a value reflecting
its “goodness” relative to other agents in the memory. You then choose to
substitute the new agent with the agent in memory with the lowest aggregate
benefit value. This time, however, it is not the case that everything has equal
weight, so instead we employ the method used in the SMARTER algorithm
- Simple Multi-Attribute Rating Technique Exploiting Ranks. This algorithm
assigns values to attributes and, by ranking the attributes, also assigns them
weights. The weights are normalized, and the aggregate benefit value is the
sum of the weighted value of each of the attributes. In fact, the above method
computes values for attributes in the same way SMARTER does. Here, the
alteration is in the way the attributes are weighted. All that needs to be decided
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is a ranking from most important to least important attribute. The attributes
to be considered, in the order of importance are as follows
1
:
Figure 6.1: Graphs illustrating value functions for attributes
1. Change in utility
2. Difference in MRS
3. Number of uses relative to the time the contact was added
4. Difference between the change in utility of the most recent trade, and the
change in utility of the best trade
5. Amount of time since the best trade occurred
The attribute values were computed using the same method as above, using
an assumption that the relationship between an increase (or decrease) in the
actual value of the attribute (for example the change in utility) was linearly
proportional to the change in computed value of the attribute (the value of the
change in utility relative to the other agents change in utility). Plainly, this
means, for example, that there is no difference in the change in value if the
change in utility is increased slightly from when it was initially low to when it
was initially high. Graphically, this is shown in Figure 6.1[9].
Some attributes however, are better when they are low. For instance, it is
better for there to only have been a short time that has passed since the best
trade - for this the value is computed in the usual case, and is subtracted from
one to represent this inverse relationship.
The weights were computed using then Rank Ordered Centroid (ROC) tech-
nique. For n attributes, ranked from 1 to n, the ROC weights are given by:
1
The order was experimented with and judged based on the percentage of trades occurring
with agents from their memory - the following order was found to be optimal
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W
i
=
1
n


n
∑
j=i
1
j


It is now necessary to investigate the results that this extension had on the
evolution of the simulation, including any changes in agent behaviour and the
level of trading.
6.3 Evaluation
In order to evaluate the effect that memory had on the evolution of the simula-
tion, two things were examined:
1. Loyalty
2. Specialisation
In addition, the number of agents that an agent could search through to
find a trade partner, which shall be termed “sight” was varied from 5 to 20 (20
being all agents in the district) with increments of 5. In order to fully see the
affect of memory on the evolution of the simulation, only 20% of agents were
able to produce both goods. Ten simulations were run for the topologies Local
Connected, Local Disconnected and Small World Network for each of the values
for sight, and for memory being enabled and disabled.
The reason for varying sight was to see if the “usefulness” of memory differed
with the number of agents an agent could search through.
We have already seen the method for characterising the level of trade -
the percentage of trade and of specialisation in the form of the continuum
ranging from pure producers to pure traders. However, loyalty has yet to be
mentioned. Loyalty is the idea of agents returning to the same trade partners.
In order to measure loyalty, an adapted Herfindahl index was utilised- an idea
from Wilhite’s paper [22]. This index is actually used in measuring industrial
concentration, but was adapted in order to reflect the information that we are
seeking. The calculation is based on the number of times an agent engages in
trade with the same partner. The loyalty for agent i can be calculated as:
L
i
=
k
∑
j=1
(100a
j
)
2
where a
j
is the proportion of all trades, initiated by agent i with agent j, and
agent j is one of the k distinct agents with whom agent i trades. The maximum
value L
i
can take is 10 000, and this indicated maximum concentration. In
other words agent i always trades with one agent. The index was calculated
for each agent in the categories heavy producer, heavy trader, and pure trader.
An average is taken for each of these categories, and this is averaged over the
repeated simulations.
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The level of trade was actually increased and decreased at different values of
sight across the topologies. However, after performing a t-test for significance,
the effect that memory had on the level of trade turned out to be insignificant
for all sight values used. Thus no further discussion of the level of trade will be
carried out.
However, there were significant differences in both specialisation and loyalty,
and these will be the topic of the following two sections.
6.3.1 Loyalty
As previously mentioned, the average loyalty was calculated for each of the
specialisation categories other than the pure producers. The reason for the
exclusion of pure producers is straightforward - they rarely if ever trade and
as such the index is misleading and unnecessary. The reason for comparing
within specialisations and not across specialisations is that the number of trade
partners differs significantly across specialisations and thus the index is inflated
for those who trade less. However, the change within a specialisation is subject
to less variation, therefore they shall be compared in an isolated fashion.
Heavy Producers
For heavy producers, the loyalty index is consistently and significantly greater
with memory than without across all topologies. This indicates that the ability
of an agent to store trade partners allows them to learn where the best deals for
them are and as such they can continue to return to their favoured partners. In
addition, as shown in the graph depicting the Small World Network in Figure
6.2, memory makes the most significant difference when sight is low. When sight
is low and memory is disabled, an agent can only search through a subset of the
population, chosen at random, in order to find a trade partner. Thus, if a good
trade partner is found, the probability of picking them as a potential partner on
the consecutive round is equal to the probability of picking any other contact, so
potential trading opportunities can easily be missed. However, when memory is
introduced, over the course of a few rounds an agent is able to “sample” a fairly
large proportion, if not entirety, of the population. Hence, if on the first round
he finds a trade partner and decides to store them, then the agent has the ability
to return to this reliable source in the consecutive round. Therefore, loyalty is
greater when sight is low since an agent is no longer randomly sampling the
population for trade partners. Instead they are learning who the best partners
are. This trend is apparent across each topology investigated.
An interesting point in the graph is the relatively sharp decline in loyalty
between a sight of 5 and 10 when memory has been employed. This is perhaps
due to the fact that this range in sight has the most significant impact on loyalty
due to the difference made between being able to search through a quarter of
and half of the population. Here, the increase in the number of potential trade
partners on each round allows for more trade partners to be found. In turn,
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Figure 6.2: Loyalty in the Small World Network, with and without memory
this increase in sight allowing agents to find more trade partners outweighs the
effect memory has on loyalty and this results in a decrease in the index.
Heavy Traders
The graphs for heavy traders actually have an intersection on each topology,
where the loyalty when using memory falls under the loyalty when they are
not. In each of the topologies this happens after a sight of 10. The reason for
loyalty to be greater with memory is the same reasoning as for heavy producers.
However, the intersection is significant in every topology except for the Small
World Network. Perhaps it would be useful to establish the reason for the
intersection at all prior to establishing the significance of the point at which
they intersect. An illustration can be seen in 6.3
As we know, agents who trade more have higher numbers of partners. In
addition, it is likely that these partners change as the simulation evolves. By
restricting himself to searching through agents in his memory, perhaps an agent
will miss out on opportunities to find new, long-lasting relationships. If the
contacts in his memory are less useful or not offering favourable deals, and he is
unable to sample the entire population of contacts (even though this is possible
when sight is 20) then he may end up making deals that are not as good with
the random sample from the population.
For example, imagine that an agent A knows a great source for Good 1, B,
with whom he trades frequently and has stored in his memory. Then perhaps,
since everybody in the population is able to search through more agents when
sight increases, someone else, C, also finds that B is beneficial to them too
- after all, the probability of someone else finding B is higher when sight is
higher. Furthermore, C is actually also better suited to B than A. Now, the
majority of the time, when A engages in hypothetical trade with B, he finds
that C must have got there first. Bs goods are depleted and even, and A and
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Figure 6.3: Loyalty in the Local Connected Network, with and without memory,
for heavy traders
B are no longer good trade partners. With no memory, this is not a problem.
A can go on to find a new long term trade partner. With memory, however,
B is still in As memory and it is likely that most rounds A will attempt to
trade with B. Of course, there will be the occasional round that A gets to B
before C, but not as often. Thus, A must either produce, or find a random and
potentially unreliable agent to trade with. This in turn means that his loyalty
may decrease as sight moves from 15 to 20 due to more competition for trade
partners, which causes agents in his memory to “expire” when they are used
less frequently. Since the majority of As contacts come from memory, and the
randomly selected agents aren’t rechosen if they are in your memory (since this
would defeat the point of the stochastic element when sight is high; it would
not truly reflect how useful memory is, as it would behave in the same manner
as sight) he is potentially left with an out-of-date memory and is hindered by
the randomness in selecting trade partners.
Now the reasoning is established, we are in a better position to consider why
the intersects differ in the Local Connected and Local Disconnected Network.
In light of the explanation, the differing intersects are fairly trivial. In a Local
Disconnected Network, competition is far higher, and closed borders means no
goods flow in or out to open up new trading opportunities. Thus sight does
not have to be as high for this problem to present itself. The graph illustrating
the intersect in the Local Disconnected Network can be seen in Figure 6.4. The
opposite applies for both the Local Connected and Small World Networks, which
displayed very similar trends.
6.3.2 Pure Traders
The Local Disconnected Network showed by far the most significant difference
between loyalty with and without memory for traders (due in part to the negli-
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Figure 6.4: Loyalty in the local disconnected network, with and without mem-
ory, for heavy traders
gible variance across simulations). However, all topologies showed a significant
difference in loyalty. For the Local Disconnected and Small World Network,
loyalty of the pure traders with memory was constantly above loyalty without
memory. The graph of loyalty for pure traders in a Local Disconnected and
Small World Network can be seen in Figures 6.5 and 6.6 respectively.
In the Local Disconnected Network, the convergence between a sight of 15
and 20 again occurred prominently between the two lines. In contrast, this
similarity was apparent in the Small World Network when sight was between 5
and 10, it widened between 10 and 15, before converging again between 15 and
20. Although convergence in the 15 - 20 region can be put down to the same
reason laid out for heavy traders, the closeness of the lines between 5 and 10
cannot be attributed to this.
Perhaps the importance of trade for a pure trader is so high that, irrespective
of whether or not memory is or is not employed, when sight is low, the benefit
of increasing it will lead to an increase in loyalty of an equal rate. This is
due to the fact that the extra agents that can be searched through allows the
discovery of good, reliable trade partners, and thus sight outweighs the added
benefit of memory. However, this is apparent in the Small World Network and
not the Disconnected Network. This is most likely due to the fact that, again,
the loyalty in the Disconnected Network suffers since closed borders mean that
there are no inflows and outflows of goods, which in turn means that trading
opportunities through direct or successive trades prevent the equal number of
changes in stockpiles of goods. This results in each agent having fewer potential
trade partners (they are exhausted more quickly due to the lack of diversity.).
However, pure traders almost always find trade more beneficial than production,
so random unreliable partners are better than none. When sight is low, and the
subset of the population to which an agent is suited to trade with in the long
term is small, the probability of choosing one of these agents without memory is
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Figure 6.5: Loyalty in the local disconnected network, with and without mem-
ory, for heavy traders
in turn low. The Small World Network seems far less affected by this - although
loyalty with memory is higher, loyalty without memory increases at the same
rate - it is simply capped by the fact that agents cannot learn.
Figure 6.6: Loyalty in the Small World Network, with and without memory, for
heavy traders
This trend of loyaly is indicative of the difference that memory makes to
agents. It helps them to organise themselves to deal only with a small subset
of the population and form long-lasting trade relationships with their peers.
This self-organisation is an important and interesting emergent phenomenon.
It better reflects reality - agents become more selective. In addition, important
thresholds were found which again emphasise the importance of initial condi-
tions on the evolution of the simulation.
Let us now move on to specialisation to see if varying sight and the addition
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(a) Pure Producers
(b) Heavy Producers
Figure 6.7: Specialisation with and without memory in a Disconnected Network
of memory alters agents decision making with respect to the interactions they
most frequently perform.
6.3.3 Specialisation
Memory had a significant effect on the pure producer and heavy producer spe-
cialisations, but no significant effect on traders, most likely due to the fact that
trading is a last resort, thus memory will not force any traders into production,
nor a significant number of producers into trading.
In the pure producer category, the percentage of agents falling into this
category was consistently lower with memory than without, again especially
when sight was low for both the Local Connected and Disconnected topologies,
Figures 6.8a and ?? respectively. Memory allowed for occasional trades - par-
ticularly at the beginning of the simulation when the rush of trades occurs -
to be stored and reused. Thus more trades occurred, most likely moving them
into the heavy producer category. In addition, as the sight was increased, the
percentage of pure producers increased. On the face of it, this seems slightly
counter-intuitive. However, more sight means more heavy producers can rely
on being selected by other agents as trade partners thus do not need to trade
themselves. This increase in pure producers occurred in each topology, both
with and without memory, before plateauing or in some cases falling slightly as
sight passed 15.
In the Small World Network, however, there was again an intersection be-
tween the two lines, where the number of pure producers with memory enabled
exceeded the number with it disabled. One good explanation for this is that
in the Small World Network, even more producers can rely on agents initiating
trade with them when sight is high, due to the freer flow of goods revealing
new trading opportunities. This bonus of the Small World Network is exagger-
ated with memory, as agents are not relying on random selection, but strategic
selection, making it even easier for pure producers to depend on being found.
Similarly, once again the Small World Network has an intersect at which heavy
producers with memory fall below heavy producers without. This shows that
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(a) Pure Producers
(b) Heavy Producers
Figure 6.8: Specialisation with and without memory in the Connected Network
(a) Pure Producers
(b) Heavy Producers
Figure 6.9: Specialisation with and without memory in the small world network
network
the pure producers and heavy producers swap at this threshold value for sight
of 12.
With respect to the heavy producer category in the Connected Network, the
percentage of heavy producers was always higher with memory, although this
difference became less significant again as sight was increased. This is due to the
fact that the opportunity for strategic selection allowing for repeated trade made
meant that some pure producers were likely to now fall into the heavy producer
category as the occasional trade they made had a higher probability of being
repeated a sufficient number times for them to pass into the heavy producer
category. However, just as the number of pure producers increases with sight,
the number of heavy producers falls. The can be attributed to the tension
between repeating trades being possible leading to pure producers becoming
heavy producers, and agents who can search through more agents meaning heavy
producers can rely on “free exchange” and becoming pure producers.
In the Disconnected Network we also witness the repetitive occurrence of
sight being 15as an interesting value. For heavy producers, it is the only time
in which the percentage of heavy producers when memory is not employed is
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greater than that when it is. This further indicates the importance of this value
of sight in the Disconnected and Connected network. At this point, there are
some agents who are pure producers and some who are heavy traders. There is
obviously considerable tension between the use of memory and the magnitude of
sight that takes effect at this point in both the Local Connected and Disconneced
Network with respect to specialisation. The tipping value for the Small World
Network, however, is lower. Here sight does not have to be as high in order for
specialisation to be affected, i.e.for agents to migrate to heavy trade. This can
be attributed to the trading opportunities that exist in the Small World Network
but not in the other two. Thus, agents have to be able to search through less
of the population before heavy producers can begin to rely on the demand of
other agents.
6.4 Conclusion
The varying of sight caused tensions between being able to rely on “free ex-
change” and more trade, and thus tensions between specialisation breakdowns.
However, there were some clear threshold values witnessed.
Self organisation was witnessed as agents began to trade with increasingly
smaller sets of the population, but the downside of memory presented itself in
the form of a constantly changing world leading to some agents being stuck with
artefacts of exchanges that had now been taken from them as increases in sight
lead to increases in competition.
The increase in competition, however, was realistic. The more global the
districts became, the more likely it was that someone could be a better trade
partner to a producer. This is akin to the real world. The more choice peo-
ple have, the more competitive the market is and the majority of the time in
business, as in the simulation, the best price wins.
It is thus not surprising that the pure traders of the Small World Network
using memory suffered the biggest hit as sight was increased from 15 to 20.
Opportunities were stolen and their loyalty declined, indicative of less reliable
trade partners due to competition and artefacts in memory as the producers
found better buyers.
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Chapter 7
Learning: Trade of
Knowledge
So far the effect of the initial topology on the evolution of the simulation has
been examined, and the agents have been seen to specialise in with whom they
engage in trade. However the evolution of trade networks has not yet been
permitted. For this, a new sort of interaction was implemented - learning. In the
simulation learning constitutes being made aware of another agent, preferably
a “foreigner” with whom it may be beneficial to engage in trade. An existing
contact in your district or memory is chosen from whom an agent can learn.
In a quid pro quo world, the agent gives up a contact beneficial to the learner,
and the learner gives one to the agent. It is preferably, but not necessarily a
foreign agent that is traded, since in the beginning it would be unlikely for an
agent to have knowledge of a foreigner that their learning partner doesn’t know
of. As the simulation progresses however, the knowledge of the existence of
agents propagates through the network leading to new opportunities and new
sufferings. Profits are made as reliable agents gain a global reputation, and
creative destruction is witnessed in this increasingly competitive economy.
7.1 Motivation
As mentioned, learning provides a way for trade networks to evolve. In essence,
it permits globalisation to evolve, employing the most efficient agents to emerge
as new trading links to the rest of the world. But we already have trading links
to the rest of world! Why is it important for these to be dynamic and adaptive?
At the moment, trading links across districts can only exist if there is a crossover
agent linking one district to another. Although this allows goods to flow around
the network, and through a series of trades can reach any agent in the world, the
crossover agents are static. Thus, they are blessed with this advantage at the
beginning of the simulation, and this remains the case throughout the entirety
of the simulation. However, the crossover agent could be poorly endowed with
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respect to its ability to produce. It could in fact a poor agent who provides no
use as a trade partner to anyone in his home or foreign district. Perhaps he
is a pure producer, the kind who noone cares to initiate trade with. In these
cases, he is blessed, for no reason other than chance, with a strategic position
which he, and noone else, is able to exploit. Surely it should be the case that
those who act as links to other districts are the best link possible. They offer
the best prices, the best quantities, they are the importers (purchase Good 1)
and exporters (sell Good 1) of the economy.
Learning allows agents to learn of an agent that may be of use to them. If
an agent is given a great source for Good 1, and his similar friend wants a trade
partner to acquire Good 1, then learning means that he can get it. Now this
great source of Good 1 is in demand by two extra agents. Those who should
be links, become links. It is no longer a random endowment. This means that
as goods spread globally around the network, agents evolve to be importers
and exporters for their district, and true efficiency in globalisation is the result.
Perhaps we could then identify more attributes of the network such as who the
most important agents are or which districts are the most important.
Let us consider why this is of interest in Economics. In honesty, it does not
get as much focus as one might think - but that is not to say it shouldn’t. The
debate over the effect of globalisation is ongoing. The aim is not to answer this
question, but instead to assess whether or not the simulation can evolve in a
way analogous to the real world, and to assess the validity of studying network
topology and evolution as a way of investigating the effect of globalisation.
7.1.1 The Importance of Structure
In the background section it was briefly mentioned that economics is focussed
very much on elements of a system as opposed to the connections between
them. This is also true when it comes to the topic of globalisation. Economic
globalisation can be seen as the act of integrating local national markets leading
to the emergence of a global market place.Globalisation shouldn’t be thought to
be a purely economic context. It is equally related to social, cultural, pollitical
and even technological emergence. However, herein, globalisation refers to solely
economic globalisation as the simulation does not capture any other concept.
Economics provides measures for assessing globalisation, or how integrated a
country is into the global market. Generally these measures include imports
and exports as a proportion of national income, the weight of how much you
export relative to imports, immigration rates and the extent to which foreign
technology is used. Ironically, these are also in economics known as flows. These
may seem perfectly viable measures of globalisation. However, whether or not
this can really tell us much about the nature globalisation is debatable. These
measures are calculated on a per country basis. It seems where these flows go
to and come from is largely ignored. Even if this break down is provided by a
country, it tells us little in isolation.
Surely it is necessary to examine the “big picture”. Where do these exports
go, where do they come from, and how are all the countries interconnected?
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Surely these questions would better enable us to assess the effects of global-
isation since seeing globalisation from a global view will allow us to analyze
dependencies and true macro trends. This is likely to shed light on questions
such as why has globalisation not benefited everyone? How has the “global view”
evolved over the past 20 years? Have political issues caused structural changes
in globalisation? Are emerging economies truly becoming integrated globally -
are they becoming central in the global network? The study of networks seems
to be invaluable here. If we can begin to understand the overall structure and
evolution of the so called global network, we can not only be better equipped
to answer these questions, but also assess whether countries , if any, are in fact
truly global. We can even begin to figure out how the network responds to
changes in political climates, how countries can become better integrated, and
perhaps even why some poor countries are still so poor.
Having established the applicability of networks to the assessment of glob-
alisation, it is necessary to assess what can be used to facilitate modelling such
a complex network. In a paper written on the architecture of globalisation,
[12] some answers that could bode well with the simulation employed were pre-
sented. This paper modelled flows of imports and exports. Countries acted as
nodes and arcs between them represented trade. Both exports and imports were
modelled this way for the years 1992 and 1998. The model was further enriched
by altering the threshold for there to be an arc between two nodes. Thus, in-
stead of having an edge between two nodes if there is any level of trade, an
edge is only apparent if the amount of trade is greater than 2% of the countries
total exports for instance. By creating this network, it was possible to assess
nodes who were central to the network, or hubs, and trends in the overall net-
work topology. This can be applied very nicely in the context of the simulation
- there are districts which can be act as countries, and imports and exports
constitute cross-district trade. Therefore the necessary data exists, enabling an
investigation into whether or not the evolution in the simulations is in any way
similar to that of our world to be conducted. In addition, whether there are
correlations between wealth and important nodes in the network will be inves-
tigated, along with whether the results are in line with the Neoclassical view of
globalisation. By doing so, it will become apparent just how applicable agent
based modelling is to the field of economics if a new perspective from complex
systems is taken on, and in addition what it can tell us about the world we live
in.
7.2 Implementation
An agent would choose an agent to learn from and they would exchange an agent
that they both (if possible) did not already know. In that round, if an agent
chooses to learn, they are not permitted to engage in trade or production since
learning should not be free, it should take time. An important thing to note is
that learning is another form of exchange. The learner does not just receive a
useful contact for free, they too have to share their knowledge of useful agents.
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This notion of reciprocal learning came from a paper on knowledge diffusion
through networks. [13] This paper suggests that a method whereby knowledge
is given away is not supportable when there is a possibility of any secondary
competitive effects that may arise from the free distribution of knowledge. In the
context of the simulation, these competitive effects are possible. For instance,
let an agent, call him a
l
be a learner, and the agent from who he is learning be
a
i
. In a gift giving world, let the agent given by a
i
to a
l
be a
g
. It is likely that
a
l
and a
i
would have similar trade partners in terms of suitability - this is why
a
l
chose to learn from a
i
after all. Therefore it is possible that the best agent
for a
l
corresponds to an agent that a
i
already trades with. By a
i
simply giving
a
l
this new trade partner a
g
, it is thus possible that now a
g
now prefers to trade
with a
l
and hence a
i
loses! However, if an agent is exchanged, although the loss
may still happen, it is more acceptable to a
i
as he gained something in return.
Hence the diffusion of knowledge of agents should be on a quid pro quo basis.
Learning was implemented through a Python script responsible for the fol-
lowing:
• Should the agent learn?
• If so who should they learn from?
• What agents should they exchange?
• Should the two agents store the agent they were given?
7.2.1 Decision to Learn
For the first question of whether or not an agent should learn, it was neces-
sary to determine what contributors we have. In addition, instead of making
learning a deterministic action, since it is difficult to quantify the benefit, it was
implemented such that depending on your situation the probability of engaging
in learning would vary. Learning facilitates an agent acquiring new agents with
whom he is suited to trade. Therefore if an agent is a pure producer, it is un-
likely that expanding his knowledge of who he can trade with is of much use to
him. Therefore the probability of learning should be fairly low. If however, we
are dealing with a pure trader who relies on good deals and reliable agents for
survival in the economy, learning should be something he is willing to give up
time to engage in.
Secondly we have the amount of time that has passed since his best trade.
If he has not achieved a good trade for a long time, perhaps this is indica-
tive of a changing environment, and perhaps he must branch out to find new
opportunities. This therefore also increases the probability of learning.
Finally we have, in the case of consumption being used, whether or not an
agent can afford to learn. If learning would cause the agent to be unable to
consume the baseline quantity of goods, which would cause him to exit the
economy, he definitely should not engage in learning since it would constitute a
sort of economic suicide. For this attribute a binary variable was employed. If
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an agent can afford the time given up in learning, it is set to 1, otherwise it is
set to 0, and consequently the probability of learning becomes 0.
A value is given to each of these contributors and they are weighted and
combined as in memory - using aggregate benefit values, and the resulting value
is the probability that an agent should engage in learning. A random number
is generated uniformly between 0 and 1. If the number is less than or equal to
the probability of learning, the agent learns, otherwise it doesn’t, and instead
goes on to choose between production and trade.
The final calculation is:
1
:
P(learning) = a × ((0.2 × b
v
) + (0.4 × t
v
))
where
a is the binary variable of being able to afford to learn, t
v
is the proportion
of time spent trading, 0.2, 0.4 are the weights assigned to the corresponding
attributes and b
v
is calculated as
1 − b
t
/t
where
b
t
is the time of the best trade, and t is the current time.
7.2.2 Deciding who to learn from and who should be ex-
changed
Upon making the decision that it could be beneficial to learn, it is necessary to
decide who you will source information from. An agent can source information
from any of their contacts, either permanent or stored in memory. The agent
searches through the foreign contacts of their contacts. It calculates the value
of each contact that it could learn of. The one with the highest value is taken
and in return, the agent finds a good contact to give to the agent it learned
from. Again the technique of aggregate benefit values is employed since there
are multiple attributes that influence the decision:
• How different your Mr’s are relative to the other possibilities
• How good the price of exchange is relative to the others
• How close your stock of goods are in terms of compatibility and trading
an optimal quantity
Let a
l
be the agent learning, and a
c
the agent who you may choose to learn
of. The values for the attributes above are calculated as follows. For MRS, you
are most suited to trade with agents with a very different MRS, so the value
1
The constants were found through experimentation to make sure learning didn’t damage
the wealth of agents severely but still had an effect on the simulation
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of difference in MRS is high if the difference is big, and low if the difference is
small. Formally,
m
c
v
=
m
c
− m
m
m
r
where
m
c
v
is the value corresponding to that difference in MRS relative to the other
agents, m
c
is the difference between the MRS of a
l
and a
c
, m
m
is the minimum
difference in MRS between all candidates, and m
r
is the range of differences in
MRS between all candidates.
With respect to the prices, if an agent is selling Good 1, he wants the price
to be high, and if he is buying he wants the price to be low. Since price is
calculated as:
P =
g
i
2
+ g
j
2
g
i
1
+ g
j
1
and MRS for agent i is calculated as:
MRS
i
=
g
i
2
g
i
1
where
g
i
1
, g
j
1
, g
i
2
, g
j
2
are the stock of Good 1 and Good 2 for agent i and j respectively.
then the price of a good always falls between the MRS of the 2 agents
engaging in trade.
Thus giving a value to the price you would exchange at, relative to that of
the other candidates can be computed as follows:
1. If a
l
would be the buyer,
P
v
= 1 −
p(a
l
, a
c
) − m
m
m
r
2. Otherwise,
P
v
=
p(a
l
, a
c
) − m
m
m
r
where
P
v
is the value corresponding to the price, p(a
l
, a
c
) is the price of goods between
a
l
and a
c
, m
m
is the minimum MRS between candidates, and m
r
is the range
of MRS between candidates.
This means that the if an agent is selling, the higher the price relative to the
range of possible prices, the higher the value. Similarly, if an agent is buying
the lower the price relative to the possible range in prices, the higher the value.
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Finally we have the value of the compatibility of your stock piles of goods.
As mentioned before, it could be the case that the MRS’s differ considerably
between two agents, but one of them has considerably more to sell (more Good
1), or alternatively more purchasing power (more Good 2). This means that the
quantity exchanged may be far less than optimal for one of the agents. They
may have been hoping to buy or sell more. The only quantity you need to be
concerned with is the quantity owned by the agent, of the good he would be
giving away. Since it is not necessarily guaranteed that the price will approxi-
mate to 1, it is also necessary to consider the price. The value corresponding to
your relative stock piles of goods is computed as follows:
1. If a
l
would be buyer,
Q
v
=
q
1
q
2
where
q
1
= min
(g
l
2
p
, g
c
1
)
q
2
= max
(g
l
2
p
, g
c
1
)
2. Otherwise,
Q
v
=
q
2
q
1
where
q
1
= min
(g
c
2
p
, g
l
1
)
q
2
= max
(g
c
2
p
, g
l
1
)
and
g
c
1
, g
c
2
are the stock piles of Good 1 and 2 respectively for the candidate agent a
c
g
l
1
, g
l
2
are the stock piles of Good 1 and 2 respectively for the learner agent a
l
and p is the price between a
l
and a
c
The final calculation for the aggregate value is the summation of the weighted
values of the attributes,
V =
3(M
c
v
)
5
+
P
v
+ Q
v
5
The agent with the highest value is who the learner learns of, and the agent
who knows this successful candidate is the learner’s partner in exchange. The
learner employs the same method to find who to give his partner. They both
then decide independently whether or not to store the agent using the method
explained in the memory section. However this time, the change in utility is
not known, so instead it is calculated as a hypothetical trade - if I were to trade
with this new learned agent, what would be my gain?
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Figure 7.1: Chart illustrating effect of learning on strategy
7.3 Evaluation
The aim is to explore, on two levels, the effect of learning on network structure,
and the evolution of trade networks. The first level is what it means for indi-
vidual agents. What new patterns emerge? Are strategy shifts witnessed and
do prices converge more readily? On the second level the focus is not on agents
but on districts. Since districts are regions of isolated agents, they act as coun-
tries or clearly defined bordered regions. Trades between regions are analogous
to imports and exports. Are there correlations between levels of imports and
exports and wealth of districts? Do all districts interact with each other? Are
there differences in the levels of imports and exports between districts? To do
this, we will introduce a notion of networks based on imports and exports. This
was applied to real countries by Raja Kali and Javier Reyes in a paper “The
Architecture of Globalisation” and the idea of networks based on imports and
exports, and comparison with my results to the real world comes from here.[12].
7.3.1 Specialisation, wealth and price dispersion
As stated previously, learning is an interaction to be performed in lieu of both
production and trade, which accounts for the cost of networking. One would ex-
pect that this new interaction results in a decline in trade, since probabilisticly,
agents who engage in trade more frequently engage in learning more frequently.
In fact, the slight drop in the average level of trade, from an average of simu-
lations using the local connected and small world networks actually resulted in
an statistically insignificant fall in trading. Trade fell by 0.8%, and due to the
variation in the percentage of trade across simulations, this was shown to be
insignificant via a means test. Thus, learning cannot be said to either increase
or decrease the level of trade in the simulation.
However, once again interesting strategy shifts are witnessed in the decisions
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Figure 7.2: Chart illustrating effect of learning on average wealth
of agents. Figure 7.1 illustrates a somewhat counter intuitive alteration of strat-
egy. It can be seen from the chart, that when learning is employed, there is a
significant increase in the percentage of pure producers in the population. It is
also apparent from inspecting this chart that there is a simultaneous drop in
the percentage of heavy producers. The other two specialisations go virtually
unaltered. From this, one can infer that with learning enabled, some heavy
producers migrate to the pure producer category. This can be explained by the
diffusion of knowledge of good trade partners through the network. As agents
are able to learn on suitable trade partners, the make new previously unreach-
able contacts from foreign districts. Recall a heavy producer would produce for
a few rounds and then trade in the next before returning to production. Now
however, as an agent becomes aware that this heavy producer can offer a good
trade, the heavy producer can rely upon trade being initiated by a pure trader.
Since the trader is likely to store this good trade in his memory, he is also likely
to return. Thus new long term relationships are formed and the heavy producer
is rarely, if at all, required to initiate trade.
Another interesting and hugely significant effect that learning has on agents
in the simulation is the effect of average wealth. Figure 7.2 illustrates a chart
showing average wealth in both the local connected and small world network.
It is clear from the chart that the addition of learning causes a large increase
in average wealth of agents. In fact, it causes average wealth to double, with
extremely low variation. This is quite remarkable, and the reason is not what
one may expect. It could be thought that this new interaction provides a way for
the traders of the world to make more profit and as such have a higher wealth,
so the increase in wealth is likely to stem from the traders becoming wealthier.
However, the distribution of wealth remains constant with and without learning.
This implies that the increase in average wealth effects the population as a
whole. Everybody gets richer, but nobody relatively richer. In other words,
learning offers new efficiencies and opportunities in trade which lead to society
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Figure 7.3: Chart illustrating effect of learning on average wealth compared to
the Global Network
as a whole becoming better off. The fact that society as a whole becomes better
off is explained by returning to a fundamental concept in the model adopted,
namely the Pareto trading paradigm. Since every agent will only engage in
trade that makes them better off, every trade makes society as a whole better
off also.
However, the interesting point is the creation of new wealth. Wealth that
didn’t exist before all of a sudden does. So this begs the question exactly
where has this wealth come from? Perhaps it is purely down to the opening
of borders. To conclude this however, we need a point of reference. Learning
moves society to a more global position, where more agents are connected to
other agents, and in essence borders are broken down. So the most suitable
point of reference seems to be the Global Network. If the wealth creation is
purely from the ability of agents to search for trade partners in a larger subset
of the population, one would expect that the average wealth with learning in
the Small World and Local Connected networks would approximate that of the
Global Network, ceteris paribus. After conducting this experiment, this was
shown to be the case. However, Figure 7.3 illustrates the effect that decreasing
the sight of agents in the Global Network to 20 (the same number of agents as
in a district), and allowing agents in the Global Network a memory of size 10
(the same as with learning), has on the average wealth. Now, average wealth of
agents with learning enabled relative to average wealth in the Global Network
is approximately 32% higher, which is also proved to be significant via a means
test.
So there is a success of the implementation of learning, manifesting itself in
wealth creation when compared with a global network with the same restrictions
on sight and memory. This can be explained by the addition of strategy and
less search. When learning is enabled, agents are able to locate through their
contacts, the best partners. This means that, although you give up time to
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Figure 7.4: Chart illustrating standard deviation from average price, with and
without learning
learn, agents in your memory are well suited to you. It also means that if
circumstances change, and someone you used to depend on no longer offers
good quantities or prices, you can learn of someone else who does. This means,
when an agent doesn’t decide to learn, and searches through its memory for a
trade partner, some of its “memory items” are of agents specifically picked to
benefit the agent in him. However, in the Global Network, agents in the memory
are simply random encounters of random trades. They may have been one off
trades, they may have been sub-optimal. The point is, when selecting randomly,
and the agents in your memory are really still a product of random but lucky
selections, the probability of finding the best agent for you in the network is low.
Hence, you are likely to make less profit from trade partners in your memory.
On the other hand, with learning, as time progresses the probability that an
agent you learn of is the best agent for you in the network increases since the
knowledge in the network increases. This leads to new, previously unwitnessed
wealth being created through strategically seeking suitable trade partners as
opposed to hoping you happen to find one.
This wealth creation can be seen as a suggestion that the argument avidly
debated on the topic of economic globalisation, globalisation makes everyone
better off, is in fact potentially correct. However, this is in a far more simple
idealised world in which barriers to trade do not exist, subsidies for local pro-
duce do not exist and so on. Nonetheless, in this ideological (and perhaps what
economic globalisation strives toward) world, it is the case that becoming strate-
gically, or intelligently global does in fact create wealth, benefiting society as a
whole on a relative scale. In addition, it is important to note that prices could
effect this conclusion. If average wealth increased and prices increased, then
the increase in average wealth would be cancelled out by the increase in prices.
However, prices were never seen to be higher when learning was employed and
thus the conclusion stands in the context of the simulation.
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Moving on to price dispersion, the chart in Figure 7.4 illustrates the massive
fall by one half in standard deviation from average price when learning is enabled
for both the Local Connected and Small World networks. This is also shown
by the graph depicting pricer per iteration, where the convergence is easily
noticeable. Since optimal trades can be made, goods flow in an efficient manner
around the network, removing price dispersion across districts to reach a stable
price with small oscillations.
7.3.2 Emerging Globalisation
Architecture
In order to measure the emergence of globalisation, networks depicting districts
as nodes and directed edges to correspond to imports and exports were created.
If district A imports from district B, then their is an arc from A to B. If district
A exports to district B, then there is an arc from B to A. This means that the
direction of arcs reflects cash flow, or the flow of Good 2.
Upon initially creating this network, with edges apparent simply if there is
trade, most countries engage in trade with most other countries. In order to
measure the centralisation of the network, the ratio of edges was taken relative to
those edges apparent in a start network of the same size, for both the import and
export graphs. The Centralisation Index thus measures the degree of variability
in the nodes of the network as a percentage of that as in a star network of the
same size.
The chart in Figure 7.5 shows the centrality at the 0% trade threshold (trade
exists) and the 5% trade level. At the 0% level, arcs exist from i to j if district i
imports from district j. At the 5% threshold, arcs exist from district i to j if at
least 5% of your imports come from district j. Centrality is shown for both the
import and export networks. The significance of the 5% threshold stems from
the fact that there are 20 districts. If every district traded an even amount with
every other district, then the amount of imports and exports from district i to
district j would be 5%.
From inspecting the chart, it is clear that as the threshold increases, the
networks become more centralised. When the threshold is at 0% every virtually
every district engages in some form of trade, be it a small or large amount,
with every other district, implying an extremely decentralised network. In ad-
dition, the index for both the imports are export networks differ insignificantly.
However, by increasing the threshold to just 5%, dramatic changes in the struc-
ture of the network occur, and the biggest change by far occurs for the import
network.
The increase in centralisation illustrates that when the threshold moves to a
more meaningful level of trade, all countries export to a small number of part-
ners. The centralisation of the import network however is far more noticeable.
When the threshold is set to a meaningful level of trade, the majority of imports
have the same destination - one of a small subset of the entire population of
districts. These districts take the bulk of imports that are exports for a large
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Figure 7.5: Illustration of Centrality as a percentage for the import and export
networks using different thresholds
number of countries. In this way, these districts can be seen to act as centers
of gravity, attracting goods to their region. This is analogous to the emergence
of a core-periphery structure, in which the core are the districts importing the
most, and the periphery the others exporting. This in turn means that the core
is in a position to exercise a large amount of influence on the districts of the
periphery.
With respect to the realism in this finding, it is actually quite astounding.
This core group of districts act in a similar way to the G8 countries, buying
vast amounts of goods from countries across the rest of the world, the periphery.
As such, the core or G8 are able to exert influence on to the periphery - the
developing world due to the dependency that these countries have on the core
of the network. This finding further enforces the power that the G8 have, and
although the simulation only deals with economic consequences of globalisation,
in the real world this core-periphery structure can explain for many things
from why political bullying works, to the fact that global decisions of world
depend on the decisions of the G8 leaders - the core of the network. It is hugely
exciting that through the implementation of such a simple method of knowledge
diffusion, structures readily apparent in the real world emerge, adding further
justification into the insights that agent-based modelling can provide to the
field.
However, the centralisation wasn’t quite as high in the import network as is
witnessed in reality. From the data provided in the paper “The Architecture of
Globalisation”, [12], the Centralisation Index was computed to be in the region
of 77%, so what is witnessed in the simulation is considerably lower, yet still
very much apparent, centralisation. This could be explained by the simplicity
of the simulation relative to the complexity of globalisation. In the real world,
we have trade barriers from taxes, some countries are wary of international
trade, especially free trade, and as such it may be more difficult to enter the
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core of the network. In addition, the most likely biggest difference is the role
of governments. Countries already in the core seek to maintain this position,
and as such can attempt to prevent countries entering so as they do not lose
out on the benefits - they do not lose their power. This notion of those with the
power can exert more power and as such keep the power is not apparent in the
simulation. Rather, it is a world in which the most efficient districts rule, free
trade promotes efficient allocation of resources, and there do not exist barriers
to entry.
This notion can be seen in two lights. One in that it is a flaw in the model
- a sign that fundamental detail is lacking. However,on the other hand exists
a more interesting and compelling argument. The model seeks only to capture
globalisation in its economic form. Perhaps the realism lacked is not a flaw
in the model per-se, rather it is an indication of the corruption by mankind
of the benefits of globalisation. Perhaps it is the complexities and unfairness
introduced by human motive and human interactions that results in a world
where countries are suppressed by others, to benefit the economic and social
well-being of those in power. This is a fairly abstract argument and as such can
benefit from an example.
Consider third world farmers, and a British cocoa distributor. They import
an abundance of cocoa from these third world farmers. Britain is a member
of the G8 - a member of the core, and the country of the third world farmer,
Ghana, is the a member of the periphery. Britain has power to buy cocoa from
the farmer for a painfully low price. This does not directly damage the farmer
- after all if it wasn’t for Britain he wouldn’t be exporting this batch of cocoa.
However, imagine Britain imports an abundance of raw materials from Ghana.
The fact that we pay such a low price prevents Ghana earning much for its
produce, and as such does not have the funds to import from countries such as
Britain and the rest of the world. It is thus unable to enter the core. One may
argue that if Ghana will accept the price, Britain should pay no more, and this
seemingly unfair price is just the result of market efficiencies. Although in some
respect this is true, it is the fact that Ghana cannot escape its dependence on
the core that is the point. It has no choice to accept this offer, as without it,
the country is definitely worse off.
So in the real world, members of the periphery being dependent of the core
forces a vicious cycle in which it is difficult to escape such dependency due to
the influence the core can have on the periphery. In the simulation, free trade
means this influence is lacking. Members of the core have no way of suppressing
the periphery - the mechanisms don’t allow for it. They rise to the top through
having earned enough Good 2 to make large purchases. If another district is
able to do this, nothing stops it. Rise of another district may take trade from
others, but this rise is possible. In reality, some governments go out of their
way to protect economic well-being in their own country, at the direct expense
of others.
A good example of this would be the American governments method of sub-
sidising local farmers, and applying heavy tariffs to foreign produce. America
is not as efficient in farming as some parts of the world, foreign countries offer
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Figure 7.6: Lorenz curve showing the distribution of links in a network
far better prices. The American government knows that few businesses will pay
more solely for the reason that it is grown in the United States, and thus they
simultaneously make foreign produce more expensive through tariffs, and local
produce cheaper through subsidies. This is an example of entirely irrational
economic behaviour in what we believe to be an increasingly globalised world.
This is in fact illustrative of the fact that we are far from truly global economi-
cally. Countries are still concerned about having dependencies on countries for
items such as food, and governments still favour the short term interests of the
national, not global population. However, the advantages of free trade as it is
in the simulation, have been hypothesised in economic theory from as early as
1871, where David Ricardo wrote a book titled “On the Principles of Political
Economy and Taxation” which bore the idea of comparative advantage. Put
simply, comparative advantage addresses the fact that free trade means that
if one nation is better in production of a good at another - it can do so with
lower cost, offering lower prices, then they should focuses their production on
this good. This enables efficiencies and prices that couldn’t be realised if the
country less efficient in production were to produce the good. America and its
farming is an example of a direct contradiction of this idea.
In addition to analysing network structure based on centrality, the Lorenz
curve was employed to enable the graphical visualisation of distribution of edges
across the network of districts. Lorenz curves were computed for both import
and export networks and can be seen in Figures 7.6 and 7.7 respectively. These
again illustrate the differences in the network structure for imports and exports.
The graphs can be interpreted in a similar fashion to those of wealth dis-
tribution. Along the x-axis we have the percentage of districts, and along the
y-axis we have the cumulative percentage of total links apparent in the network,
stemming from these districts.
The graphs further highlight the more uneven distribution of edges in an
import network - with a few nodes holding the majority of the edges, juxtaposed
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Figure 7.7: Lorenz curve showing the distribution of links in a network
with the export network which is far closer to an equal distribution. This is a
perhaps simpler graphical way to understand the effect of a more centralised
network on import and export networks. Again the distribution is far more fair
than that of the real world, for reasons already discussed.
Correlation between wealth and deficits
In economics, on of the measures of economic integration is the looking at a
countries trade balance. The trade balance of a country is simply its exports
minus its imports. If the trade balance is positive, it is known as a trade
surplus - you export more than you import; if it is negative, it is known as a
trade deficit - your import more than you export. Traditionally, in economics a
trade deficit is thought of as a bad thing, although this is not set in stone. In the
simulation however, the opposite was consistently true. A trade deficit always
led to higher wealth. Instead of a trade deficit being an indication of high debt,
it is an indication of power. The reasons for this trend in the simulation is two
fold. Firstly, debt doesn’t exist and as such, a trade deficit says nothing about
the debt of a country. Instead it reflects that the country is in a position spend
money to buy more goods and create more wealth. As previously discussed,
the greater wealth cannot be attributed to the prices differences, since these
are negligible across districts. However, although the simulation does not have
debt, it does not imply that this observation is unrealistic. On the contrary
it turns out that the wealthiest and most powerful countries of the world have
the largest trade deficits. Judging by what we have witnessed in the import
networks, this is hardly surprising. The core of the network are destination for
the majority of imports, and the core of the network in the real world is the
G8. The G8 import the largest quantity of goods, and thus have the largest
trade deficits. The reason for the high level of imports is out of the scope of
this project, however, it is likely that the trade deficit is not just an indication
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of the a countries level of debt, GDP growth or unemployment, but also a good
estimator of its position and role in the international trade network.
Creative Destruction
We have witnessed that districts rise to a position in the core through the diffu-
sion of knowledge of agents offering the best deals. What has been overlooked
however, are these new bridges, and the importance of these new cross district
traders in the emergence of globalisation. In fact, inspecting this gives some
fairly exciting results. For clarity, to demonstrate the results, one simulation
will be looked at.
Creative destruction is a notion in economics to do with innovation. It
describes the process by which innovation can result in entrepreneurs entering
the market place and fueling economic growth, despite it destroying value of
other established companies. In the context of the simulation, this can be seen
as an agent losing their position in a market place to a more proficient agent.
Although the agent who suffers from this, and his wealth may well be reduced, it
is this process that makes society as a whole better off. An agent should not be
given a valuable position in a market place if they are inefficient. Recall one of
the things learning sought to eradicate was the unfounded fortune of crossover
agents. They, for no reason, enjoyed a position in the market, that firstly they
may not be able to fully exploit, but secondly, do exploit despite there being a
non-crossover agent who could do it better.
Figure 7.8: A crossover agent and his trade partner
In order to illustrate this pictorally, a graphic from the simulation was ex-
tracted. It may look like there are few trades, however, the image is of only one
iteration. This is to make the arcs more clear however also means the extent to
which creative destruction occurs is lacking. In the simulation, the trade occur-
ring between the crossover agent and the foreign agent occurs more than once.
2
.
The image provided in Figure 7.8 shows a crossover agent (highlighted in red)
2
A temporary output to CSV was implemented purely for the purpose of looking for creative
destruction, and this was studied to decide which simulation to use as an example.
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and its trade partner in black, near to the beginning of the simulation - at 50
iterations. Notice that this crossover agent has an arc entering it, representing
a trade (not necessarily initiated by him). Other agents in the district do not
trade much with agents outside the district, we are close to the beginning of the
simulation and knowledge has not been propagated across the network.
Figure 7.9: The fall of the crossover agent and the new trade partner
Figure 7.9 shows the same simulation, only this time 500 iterations later.
By this time, a fair amount of knowledge has diffused through the network and
agents are more strategic about with whom they engage in trade. Now three
agents are highlighted, the crossover agent again in red, and in addition a non-
crossover agent in blue and the trade partner in black. Notice that the node that
had an arc from itself to the crossover agent (highlighted in black) now have
none to the crossover agent, and instead one to the new agent. This new agent
has emerged as a more efficient and effective trade partner, with better prices
and more to offer. Also notice that this new district bridge is not a crossover
agent. In fact, for the duration of the simulation, the once powerful crossover
did not engage in cross district trade again.
Not only does this illustrate that learning has provided new efficiencies to
be witnessed, but in addition is an indication that creative destruction is not
a notion that requires innovation necessarily. In the simulation, there is no
concept of innovation, yet this is still witnessed. Rather, creative destruction
can also be realised through free markets and free trade. They allow for those
who are most proficient in a job to rise to that job. As such, not only do they
become more wealthy, but the wealth of society as a whole is increased due to
better prices and quantities being available to other agents.
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7.4 Conclusion
Learning has proved to be successful in facilitating the proliferation of knowledge
through the network. In addition, it has allowed for globalisation to emerge in
a more decentralised manner than the real world, yet still with a clear core-
periphery distinction. Questions have been raised about the trade barriers in
the real world perhaps preventing the benefits of globalisation to in fact be felt
globally. Unfortunately, further investigation into answers to these questions
are out of the scope of the project.
Creative destruction has been witnessed as agents who deserve a position
facilitating global trade have earned them through reputation and reliability,
and it is suggested that the notion of creative destruction need not be restricted
to the requirement of innovation being the causal factor. For further justifica-
tion to this argument, we can revisit the American farmers. If the American
government were to engage in “laissez-faire” economics - leaving the economy to
market mechanisms by refraining from government intervention - then it is virtu-
ally definite that a large portion of the American farmers would be bankrupted,
and better, cheaper providers of the same good could take their place. However,
this brings us to the limitations of mankind to the progression of globalisation.
Free trade requires trust, and it requires governments to act in the best interest
of the world, not solely their nation. As such, unlike in the simulation, some of
the efficiencies, fairness and advantages of globalisation cannot be realised for
everybody. Flaws in ourselves hamper the realisation of benefits in becoming
truly global.
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Chapter 8
Evolution as a method of
gaining insight
In the simulation, evolution can be employed in order to gain insight in to the
model. It allows a user to see what makes a fit agent - what character(s) does
the genetic algorithm cause agents to evolveinto given the initial conditions of
the simulation? This provides insight into what effect initial conditions have on
the evolution of the simulation, and under which particular conditions certain
strategies are optimal for agents. It is important to note that it is not reflective
of biological evolution. Instead, the genetic algorithm creates a new population
from the current population, and the current population exits the simulation.
This process is repeated to evolve an increasingly fit population, and each new
population is examined with respect to the others to find general trends in the
evolution of agents.
Let us begin by explaining in detail how the genetic algorithm works, specif-
ically with respect to the simulation.
8.1 Genetic Algorithms
Genetic algorithms encode a potential solution to a particular problem, and
the method of attaining this solution is analogous to that of evolution. In the
Background section the reason that evolution is such a good method for complex
optimisation problems in large design spaces was explained.
The genetic algorithm begins with a population of randomly generated agents.
These agents are allowed to produce, trade and so on for a period of time. Each
agent is then assigned a value based on its fitness for solving the problem; in
this case, problem solving ability is gauged according to how high their util-
ity is and how wealthy they are. It may seem that utility and wealth are two
ways of displaying the same thing. However, since prices can vary, and are not
necessarily 1, measuring wealth also captures value. This means an agent with
a relatively large stock of goods who has a lot of Good 1 can be considerably
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wealthy if the price of Good 1 is high, i.e. if Good 1 is in high demand. There-
fore it is necessary to consider both sides - utility and the value of their assets.
Upon each agent being assigned a fitness value, agents are selected for breeding.
The probability of a fit agent being selected is higher than that of a worse off
agent, but the worse off agent still has a chance of being selected to breed. Each
agent that successfully makes it through (an agent can make it through multiple
times), is randomly chosen a partner with which they will be bred. This pair of
agents, to whom we will henceforth refer as parents, are then bred to generate
two new offspring using a process of crossover and mutation. These offspring
make up two agents of the new population. Once the new population contains
as many agents as the first population, it is initialised and the first round of
the genetic algorithm is complete. These agents then produce and trade and so
on until they are evolved into the next population. The process continues for a
finite amount of time specified by the user.
8.2 Implementation
Firstly, we have to define what changeable aspect of an agent should be consid-
ered. This will determine what is bred between the 2 agents. The following is
what is evolved:
• Amount they can produce of Good 1
• Amount they can produce of Good 2
• The size of their memory
• How many agents they can search through to find a trade partner
And the fitness of agents is determined by:
• Wealth
• Utility
The new population will be the same size as the initial previous population.
Next, the implementation of the genetic algorithm will be explained and this
will cover the stages below:
1. Assign a fitness score to each agent
2. Pick, based on the fitness scores, the agents that make up the parents of
the new population
3. Generate the offspring for each set of agents
4. Initialise the new population, and run restart the simulation
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8.2.1 Fitness Scores
As in the case of memory and learning, the multi-attribute problem leads us to
generate values for each of the two variables, wealth and utility, and combining
the weighted values to attain a fitness score. The value for wealth and utility
are calculated as follows. A value closer to one is used for high utility and high
wealth:
• Value for utility for agent i
1
:
U
i
=
v
i
µ
where
v
i
=
u
i
− u
m
u
r
µ =
∑
n
i=1
v
i
n
and
u
i
is the utility of agent i, u
m
is the minimum utility of the population, u
r
is the range in utilities, and n is the number of agents in the population.
• Value for wealth for agent i, W
i
is the same for that of utility, but substi-
tuting utility for wealth.
The aggregate value for an agent is given as:
V
i
= 0.6 × U
i
+ 0.4 × W
i
Then, each agent is assigned a new value, as a proportion of the total values
of all the agents. Formally:
F
i
=
V
i
∑
n
i=1
V
i
where
n is the total number of agents.
F
i
therefore describes what proportion of the total fitness of all the agents
agent i has, which is used in selecting the agents to breed.
8.2.2 Agents to make up the new population
Now each agent has been evaluated in terms of its fitness relative to other agents,
and has been given the proportion of the total fitness that his fitness represents,
it is possiblez to generate a new population. As previously mentioned, even the
less fit agents have the opportunity to breed. The selection process is achieved
through employing a technique known as roulette wheel selection. Roulette wheel
selection works by giving fitter agents a higher probability of being selected, and
1
In the canonical genetic algorithm the fitness score is the evaluation of the agents fitness
over the average evaluation[15]. For a detailed tutorial on genetic algorithms see [15] in the
bibliography.
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poorer agents a lower probability. It works as follows. Imagine the total of the
values,
V =
n
∑
i=1
V
i
to be a pie, and each agent’s proportion of total fitness,
F
i
=
V
i
V
to correspond to a share of this pie. If an agent has F
i
= 0.1, this indicates
that he is entitled to 10% of the whole pie. Each agent now has a slice of the
pie, and the size of the slice corresponds to their value of F
i
. Now, we rearrange
the agents in terms of the size of their slice, in ascending order. Each agent is
also now ranked by its index in this new ordered list from 0 to n. We now have
a pie that looks something like Figure 8.1.
Figure 8.1: Illustration of a pie corresponding to a set of 6 agents
Selection is carried out by generating a random number, and the agent whose
range captures this number is selected to go through. The range that each agent
has depends on its score and its rank. Formally, the range, L
i
to T
i
belonging
to agent i with rank r and score F
i
is given by:
L
i
=
r
∑
j=0
F
j
T
i
= L
i
+ F
i
Random numbers are generated, and the corresponding agent is selected
until the number of agents selected is equal to the number of agents in the
new population. Each agent in the list of “successful” agents is now randomly
allocated another agent to be its partner. Once every agent has a partner,
offspring are generated.
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Figure 8.2: An Illustration of crossover between two agents P1 and P2 gener-
ating children C1 and C2 based on random number r
8.2.3 Generating offspring: Crossover and Mutation
The next step of the algorithm is to generate the new population of agents. As
a reminder, the genes that characterise an agent are:
• Amount they can produce of Good 1
• Amount they can produce of Good 2
• The size of their memory
• How many agents they can search through to find a trade partner
Each of these is an integer, and thus can be represented as a binary string.
Concatenating these strings gives us the “DNA” of the agent, as shown in Figure
FIG HERE. Crossover is the act of combining the DNA of both parents to
generate offspring. Here I use a method known as uniform crossover. Here,
each of the two children have an equal probability of inheriting a single bit from
a particular parent. Let P
1
and P
2
be the two parents, and C
1
and C
2
be the
children of those parents. For each bit in the DNA of the parents, generate a
random number r
i
.
• If r ≤ 0.5, then the ith bit of P
1
corresponds to the ith bit of C
1
and the
ith bit of P
2
corresponds to the ith bit of C
2
• Otherwise, the ith bit of P
1
corresponds to the ith bit of C
2
and the ith
bit of P
2
corresponds to the ith bit of C
1
Figure 8.2 gives a graphical example of crossover between two agents. In
reality, not all combinations are valid. For instance, if the upper bound on how
much an agent can produce is 30, then 5 bits are needed to encode all possible
values. However, this gives 31 possible values. Therefore checks have to be
done to ensure the value realised is with in the bounds. In addition, if the
upper bound is 30, but the agent can only produce 10, in binary this would be
1010 which is only 4 characters long. In this instance, this would be padded to
01010.
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The next step is mutation. The mutation rate is the probability that a
particular bit will be flipped, and in the simulation is set to 0.07. For each bit
of the children, generate a random number uniformly in the interval [0,1). If
this is below the mutation rate, flip the bit and move to the next bit, otherwise
simply move to the next bit and repeat the process. The bit string is then split
up back into the 4 attributes that characterise the agent.
Having generated the genes for the new population, they are intialised. The
number of crossover agents in the new population will be equal to the number
in the initial population and which agents become crossover agents is decided
randomly.
8.3 Evaluation
Simulations were conducted and agents evolved in order to gain insight into the
model, particularly to determine whether restricting the production of goods,
learning and memory increased the value of trade or simply made it necessary
or more available. This can be achieved through analysing the level of trade as
well as strategy shifts displayed in trends of specialisation of agents. In addition,
changes in both wealth and its distribution are examined.
Without any of the extensions made to Wilhite’s original model, the genetic
algorithm caused agents to become pure producers. In addition, trade fell to
0.8%. This is illustrative of how much better production intrinsically is in this
model. Agents do not need to change, and the lack of necessity for trade in
the population means agents simply become proficient at production and the
production functions of agents tend to their maximum. This is due to the fact
that there is nothing but production functions to vary and, as such, little scope
for any further direction of evolution.
Memory and learning, however, offered more interesting turns of events. The
evolution of agents is very similar in both circumstances, but differences in the
specialisation of agents is apparent.
Let us begin with the similarities, namely wealth distribution and average
wealth of society. For both learning enabled and solely memory enabled, the
wealth distribution in society becomes incredibly even. Figure 8.3 illustrates
this, as the Gini Coefficient falls sharply in the first four iterations of the evolu-
tionary algorithm. As agents evolve, production functions are optimised. Agents
tend towards having very similar abilities, particularly in production, despite
the mutation employed in the algorithm. This means that the distribution of
wealth practically reaches perfect equality - convergence happens too readily.
In addition, the average wealth of society increases; indeed, over the course
of the algorithm it is actually doubled, as illustrated in 8.4. Again, this can
be contributed to the proficient producers that develop. The possibility of it
being attributed to efficiencies in trade from the employment of memory and
learning can be dismissed upon inspecting the graph describing the level of trade
when learning is enabled. The amount of trade falls rapidly within the first 4
iterations of the algorithm before levelling off, shown in Figure 8.5. With a
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Figure 8.3: Change in distribution of wealth, measured by the Gini Coefficient,
as the genetic algorithm progresses
Figure 8.4: Change in average wealth as the genetic algorithm progresses
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Figure 8.5: Change level of trade as the genetic algorithm progresses
Figure 8.6: Change in agent specialisation as the genetic algorithm progresses
world of proficient producers, trade simply is not necessary. There is less value
in trade than there is in production, and as trading has always been a last resort,
the algorithm works to remove this flaw which acts only to restrict equality in
the economy.
This shows that as the evolutionary algorithm progresses, since the traders
are the poorest agents, often by quite a long way, the probability of them getting
through to the next round begins to fall. However, this does not address the
question of where they actually grow.
This can be seen by examining the specialisation of agents. Figure 8.6 shows
the specialisation of agents with the progression of the evolutionary algorithm.
As agents evolve, the pure traders and heavy traders disappear. They are
no longer worthy of existing in the economy. However, like with memory or
learning, this time it is the heavy producers that triumph. All agents evolve
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Figure 8.7: Comparison of change in agent specialisation evolving with and
without learning
to favour production, but the percentage of pure producers actually declines,
as heavy producers replace both pure and heavy traders, and pure producers.
Comparing the breakdown in specialisation at the end of the simulation with
learning to the those with only memory, a fairly large difference is apparent.
This can be seen by inspecting Figure 8.7. In both contexts, by the time the
genetic algorithm is finished, there are no pure traders and a negligible number
of heavy traders. However, learning has proved its success in facilitating trade
networks. Despite there being only a small increase in the evolved level of trade
when learning is employed, is significant (via a means test) when compared
with the level of trade with just memory. From Figure 8.7 you can see that
with learning, there were fewer pure producers in the end. This is indicative
of the fact that learning offers beneficial trading opportunities. This in turn
means that although agents are evolving to become producers, learning offers
more opportunities for trade through the ability to both remember and seek out
a trade partner. It seems that learning is the extension that makes the most
difference to the value and potential benefit of trade.
8.4 Conclusion
In conclusion, the genetic algorithm validates the idea that production is un-
equivocally favoured, and that the evolution of the simulation is largely based
on the ability of agents to produce goods. Nonetheless, it seems the ability of
agents to learn permits some value to be added to trade. Agents production
functions do not necessarily evolve to be 30, as some agents can rely on the
occasional trade. The fact that production functions are higher also means that
trades that take place can be with bigger quantities and, with learning, with a
bigger quantity. This in turn means that fewer trades have to occur in order to
even out stockpiles and maximise utility.
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The results also highlight the need to create value of trade in the simulation,
and this is to be addressed in the following section.
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Chapter 9
Implementation
The application is a web application implemented using a combination of Java
and Python for the back end and HTML, Javascript and CSS for the front
end. The application is split up into three main sections: simulation, user
interface, and analysis engine. The user interface is the users access point and
allows creation, running and downloading results of a simulation. The analysis
engine is responsible for data analysis, producing graphs, charts, tables and PDF
generation. Both of these sections will be discussed in detail in the following
section, however for now our focus lies on the implementation of the simulation.
9.1 An Alternative Design Choice
One of the aims of the project undertaken was the formulation of a piece of
software that offers a novel approach to the design and implementation aspects
of constructing an economic multi agent simulation. For this reason, although
research was carried out on alternative platforms that could be leveraged, it was
decided not to use these since it would remove the opportunity for experimen-
tation with the implementation.
However, in this section the most appealing platform studied will be outlined,
namely JADE. This is a well established Java based platform and has extremely
impressive features as well as a diverse range of applications.
9.1.1 JADE
JADE is a platform developed entirely in Java that enables the construction
of multi agent system. Each agent is run on its own thread, concurrency, par-
allelism and cooperative task scheduling being handled by JADE. Agents can
be physically distributed on hosts and on each host there is only one Java ap-
plication being executed. Agents communicate with one another via message
passing with Foundation for Intelligent Physical Agents Agent Communication
Language (FIPA ACL) being the language of choice. FIPA ACL also allows
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the inclusion of user-defined message parameters where the semantics are not
defined by FIPA enhancing extensibility and ease of customisation. [31]
In addition to taking care of the majority of distribution and threading
issues, JADE also offers an extensive GUI. It allows the user to manipulate the
system at run time through the ability to start, restart and stop agents. In
addition agents can be tracked through message sniffing during the simulation
allowing the exposure of the internal state of subsets of the system. It also offers
assistance in debugging techniques which are often complicated when dealing
with distributed systems. An example would be the Dummy Agent which allows
inspection of message exchange between agents. It enables validation of an agent
description prior to integration in to the MAS and in the event that an agent is
malfunctioning the Dummy Agent facilitates interrogative testing. In addition
it is possible as the user to construct, send and receive messages from agents in
the simulation. [30]
However, JADE’s focus is primarily on the physical distribution and compu-
tational autonomy of agents. Although this is appropriate for the implementa-
tion of MAS, in the model I am extending, the architecture is less appropriate.
This is due to the fact that in my model, agents get to pick an action sequen-
tially, and rounds are repeated iteratively. Hence the concept of message passing
and real autonomy is somewhat redundant with respect to the synchronous sin-
gle threaded architecture I planned on undertaking. It may be viewed by some
that you are not creating a truly autonomous MAS without having physical dis-
tribution of computation and true agent autonomy. However, I believe, having
done research in to this debate that it is purely an implementation issue and
with the timescale at hand, and the model being implemented, it is reasonable
to adopt a method of pseudo autonomy with no physical distribution. I believe
the implementation choice will have little to no impact on the result of the simu-
lation since the logic by which agents make decisions are homogeneous between
the two options.
9.2 The simulation: Java & Python
Agent Based Modelling generally requires the use of Object Oriented program-
ming in order to be able to model agents and their environments as entities.
Hence, the two languages that the simulation is to be written in are both object
oriented.
9.2.1 Java
Java is to be used to model the artificial world and will be primarily for data
storage. The Java section of the application defines what an agent is, what
a world is and what a district is. The idea of the Java code is that it is the
core of the simulation - a description of what it is and not the way in which
agents interact with each other. The reasoning behind this is that these are
attributes of the system that are not to be experimented with, and should
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remain unchanged across simulations. The logic contained in the Java code is
purely “safety logic” in that it facilitates functionality with no impact on the
result of the simulation. However, the project is somewhat experimental. There
is a need to try different ways of agents interacting. For instance, in the initial
model, agents have a choice of only two interactions, production and trade. As
this is extended and more interactions are added, it is desirable not only to be
able to draw comparison between the two, but also to avoid the loss of the other
more simple set-ups I implemented. It therefore seems that there is need for a
dynamic scripting language, namely Python.
9.2.2 Python
Python is an object-oriented, dynamically-typed interpreted language. It allows
for great flexibility as well as the bonuses of object-oriented design. It is also
easily integrated with Java projects through the use of Jython
1
. In the projects
objectives it was noted that one aim of the project was to allow for further
work to be carried out. Jython allows just this through enabling embedded
scripting, i.e. end users are able to write scripts to enhance functionality to the
application.[28] Not only is this useful for users or developers in the future, but it
will also be so during the development of this specific project. The use of Python
will allow to turn extensions “on” and “off” as previously mentioned through the
use of loading different scripts or not loading various scripts describing the logic
of the simulation. Another incentive to use Jython is that time is of the essence
for this project and for it to be useful to other users it should be as efficient
as possible. It is therefore imperative to work with a language that increases
developer productivity. Python programmers are typically 2 - 10 times faster
than Java programmers. Scripts will be used for all interactions of agents:
• Trade: Search, and Negotiation and Exchange will be separate
• Production
• Initial endowments
This allows for the experimentation with regard to how agents make their
decisions and select partners etc.
The scripts prevent loss of more simple or different simulations and allow far
easier experimentation as well as simply providing organizational enhancements.
They make it simpler to run different simulations with different configurations of
logic in order to facilitate comparisons across observed macro behaviour relevant
to simulations of different scope or logic.
1
Jython is an implementation of the high-level, dynamic, object-oriented language Python
seamlessly integrated with the Java platform.
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Figure 9.1: Overview of package structure
9.2.3 Architecture
The application was designed with both extensibility and configurability in
mind. The class structure of the simulation only can be seen in Figure 9.2,
and the package structure of the entire application is illustrated in Figure 9.1.
Initial Model
The Simulation class is responsible for running iterations of the simulation and
creating objects to store data. It also acts as an interface to the analysis engine
by retrieving information that it may need (such as configuration options). The
simulation contains a world which is made up of districts and also houses the
script engine. The world is subtly different from the simulation. One way of
viewing this difference is that the simulation can be considered to run the world.
As has been indicated, the world contains districts, and districts contain agents.
In the simulations, Agents are simply actors in the economy. They know how
much they can produce of each good, they know where they live, and they know
how many people they can search through to find a trade partner.
It can be seen that Agent is a class that has solely a location, and an iden-
tifier. A specific subclass of Agent is Worker - this defines an agent who can
be active in the economy - they also have a stock of goods and an amount they
can produce of each good. If someone were to extend the model to account for
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Figure 9.2:
Reduced Class Diagram for the Simulation (package
ecosim.simulation)
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retired agents or any agent inactive in the economy, but existing in the world,
this could be achieved simply by subclassing agent. In addition, there is an
abstraction between an Agent and a Decision Maker illustrated by the fact that
Worker implements Decision Maker whereas Agent does not. This could allow
for extensibility again in the sort of agents existing in the world. For instance, if
Children were introduced and Parents supported Children, then Children may
not be required to actually do anything for a given period and the architecture
would easily allow for this.
In the class diagram the Script Engine is evident. This is the only place in the
application which actually deals with Jython - the interoperability layer between
Java and Python. This encapsulates the scripts, and also holds the responsibility
of loading the correct scripts on the basis of the simulation configurations, as
well as the packing and unpacking of arguments for interoperability. This allows
for the details of configuration and interoperability to be self-contained and thus
hidden from the rest of the application, which only interfaces with the Script
Engine, meaning it can call the same methods irrespective of the scripts loaded
for a particular interaction.
Consumption
Consumption was implemented quite simply by a supplementary Python script
which accounted for the fact that an agent, when deciding to produce or trade,
also had to consume a stock of goods. The quantity to consume is kept in the
script as a global variable in the interpreter and is set prior to running the
simulation. The script engine on construction is given a Boolean determining
whether or not consumption is “on” in this simulation and loads the Python
script accordingly. Again, when an agent has to perform an action, it calls the
same method irrespective of whether or not they are consuming.
The only additional implementation in the simulation was the fact that
agents can now become inactive in the economy - suffer an economic death,
and that consumption should be recorded. Thus the script returns an object
containing whether or not the agent dies, and if he did die he adds himself to the
list of economic deaths of its district. The district removes the agent from its
inhabitants and the simulation records the agents death in the appropriate data
store. The script also stores the quantity that the agent managed to consume
on a given iteration.
Memory
Memory allowed agents to choose whether or not to remember a certain ex-
change with a particular agent. Upon performing an action, if the action was
exchange, the agent had an opportunity to remember its occurrence. In addi-
tion, learning employed the use of memory. When an agent learned of another
agent, they had the opportunity to store this agent in their memory. The deci-
sion to learn was implemented using a Python script.
If the contact exists in the agents memory, the memory event would be
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Figure 9.3: Reduced Class Diagram for the Memory Extension (package
ecosim.simulation)
updated. Otherwise, the agent had the option of storing the event as a new
event (a new agent) in its memory. A Python script implements the decision to
store an agent. It takes care of whether to store them, and if the memory is full,
whom replace with the new agent. All it creates, however, is a Decision object
- it in no way actually performs addition, removal or updates on the memory.
This is encapsulated in the Memory object of the agent.
The addition of memory required a “sub-architecture” for storing a memory
item. This is illustrated in Figure 9.3. Every agent has a memory, and each
memory has a maximum number of events it can store. It also has a list of
remembered events - EventRecords. An EventRecord models a memory about a
single agent. It holds a reference to who the agent is, when they were added and
how many times it has been used. These are used in calculating the aggregate
benefit value of a specific memory item when determining who to store, and if
necessary who to swap. It also stores two objects called ExchangeEvents. An
ExchangeEvent is representative of the occurrence of exchange. It records the
change in utility it generated, the time of occurrence, and the quantity of goods
exchanged as well as the price. As stated, two exchange events are stored - one
for the most recent exchange with the given contact and the other for the best
exchange with the given contact.
As mentioned, the addition, removal and updating of events from an agent’s
memory is the responsibility of the memory itself. This encapsulates the logic so
that the agent can just give a decision to its memory, and the memory handles
it itself.
Evolution
The algorithm for evolution was previously explained in detail. As a recap, the
simulation runs for a fixed number of iterations. Then each agent is given a fit-
ness value based on its utility relative to the population. The fittest agents have
a higher probability of being selected than the less fit agents. For a population
of size n, n agents are selected from the current population (these need not be
distinct). These agents, let us call them successful agents, are then randomly
put in to pairs. These pairs are Parents. Each pair is bred to generate 2 offspring
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Figure 9.4: Reduced Class Diagram for the Evolution Extension (package
ecosim.simulation)
using a technique called uniform crossover (and also performing mutation), and
the offspring of all the Parents constitute the new population.
Evolving agents is initiated by the Simulation class since it is aware of the
current iteration. However, the repopulation and “resetting” of the simulation
- including replacing inhabitants of districts, and assigning crossover agents a
crossover district, is delegated by the World class.
The algorithm for generating the pairs of agents to be parents is implemented
as a Python script. The crossover and breeding of agents again introduces a new
Java “sub-architecture” which is illustrated in Figure 9.4. The Python script
passes back a list of Parent objects. The world takes this list and instantiates
a new Breeder object. The breeder objects has the list of parents but also has
the upper and lower bounds for production, sight and memory size in order to
ensure correctness in the crossover process.
The Breeder object generates a list of Children that it sends to the world.
A Children object stores the two offspring Child objects of a pair of agents in a
Parent. A Child is not an actual agent at this point, it is just the parameters to
set up the agent. When the world receives the list of children it is transformed
in to a list of workers and crossover workers. The number of crossover workers is
the same as at the beginning of the simulation and an agent is randomly chosen
to be a crossover worker.
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9.3 PDF Generation
PDF documents were chosen as a method of output as it is an effective way of
generating a neat report of a simulation. The idea was for it to contain enough
analysis in order to perform a proper evaluation of a simulation. The PDF
documents contain:
• All information used to configure the simulation
• Graphs illustrating the amount of production and trade over the simula-
tion as well as this as an actual percentage
• Graphical illustrations of trades occurring at quarter points of the simu-
lation (an illustration is given in Figure 9.5)
• Information on wealth and distribution, specifically:
– Formula for calculating wealth
– Average global wealth at the end of the simulation
– The Gini Coefficient at the start, middle and end of the simulation
– The Lorenz Curve at the end of the simulation
– A graph illustrating global wealth over time
– A graph illustrating wealth per district over time
• Information on utility including a graph of global utility over time and
utility distribution at the end of the simulation
• A table giving average prices on a district and global level together with
standard deviation, and a graph of prices over time
• Information on imports and exports of districts, specifically:
– A table showing the value and quantity imported and exported for
each district together with their trade balance
– A table showing the percentage of district i’s exports that go to each
district, for i in 1.. #districts
– A table showing the percentage of district i’s imports that come from
a certain district, for i in 1.. #districts
• A Pie chart illustrating the percentage of agents falling in to a specializa-
tion category
• Information on individual agents, specifically for:
– The wealthiest and poorest agents
– The agent with the highest utility belonging to each specialization
category
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– The poorest and wealthiest crossover agents
Each of these has a table containing data as well as graphs illustrating
the agents movement of goods over time, and consumption of goods if
applicable.
• A graph showing deaths over time, again if applicable
PDF generation was performed using the library iText. A document is in-
stantiated, and to it Chapters are added. Sections are added to Chapters, and
Paragraphs, Tables and Images are added to Sections. The document is then
written to an output stream or a file. The architecture for generating the docu-
ments was divided in to three main sections. One class, the PDFGenerator, was
responsible for adding elements to the document. The graphers were responsible
for generating charts to be added using the Java library JFreeChart. Graphers
further specialized in the sort of data they graphed for example, was the data
to do with production or trade, or perhaps individual agents? Each grapher
implements the class IGrapher. This required a method “createSeries” which,
given an enumeration of the graph to be generate, calls the necessary method
and returns you the chart.
In addition to graphing, there were also classes that dealt with general statis-
tics, such as averages, standard deviations and so on. Finally there was the class
that draws the illustrations of trade for the agents. Crossover agents are rep-
resented as orange dots. An arc between two dots illustrates a trade in that
iteration. The graphics were generated using Java Graphics. Coordinates for
agents were calculated and stored. If a trade occurred between two agents in
that round, an arc is drawn between them. The coordinates for the start and
end point were simply the coordinates of the agents, and the control point of
the arc, a point through which the curve must pass, was generated using an
elliptical formula.
9.4 Interface
The interface serves purely as an area in which to configure the simulation.
Originally, it also displayed graphs, but as the implementation progressed, the
richness of the PDF documents generated outweighed the need for the interface
to deal with anything other than configuration. In order to keep the interface
as simple as possible, It seemed better to remove the graphs in favour of solely
offering the ability to download the simulation in PDF form.
A partial screen shot of the interface is given in Figure 9.6. Care was taken
to restrict the amount of manual form entry by the user as much as possible.
This was achieved through both the use of radio buttons and check boxes where
applicable, and also by automatically hiding unnecessary configurations depend-
ing on the current options selected. However, for elements such as the number
of agents, manual form entry was necessary, so validation was implemented in
the interface to ensure that certain constraints had been met. For example,
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Figure 9.5: Illustration of a trade network for one iteration
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Figure 9.6: Partial Screen shot with all specific configuration hidden
ensuring that the number of agents was greater than 1, and that upper bounds
were greater than lower bounds and so on. Validation by alerts is illustrated in
Figure 9.8. To make the amount of configuration options less overwhelming to
the user, they were hidden and shown when necessary. Comparing Figure 9.6
with Figure 9.7, it is apparent that in Figure 9.7 there are more options in the
“network topology” section outlined in red.
The plain style of the interface helped create a more user friendly configu-
ration screen. However, it is important to realise that some of the terms are
ambiguous to first time users, thus a help section acting as a glossary of terms
must be added.
9.5 How it works
For clarity a flow diagram has been provided (Figure 9.9) illustrating the work-
ings of the application, which should help the reader to understand the following
explanation.
The simulation is created from the web interface, with the user configuring
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Figure 9.7: Partial Screen shot with some configuration options revealed (high-
lighted in red)
their simulation by turning options on and off, specifying the number of agents
and districts and so on. On pressing “Create”, these configuration are sent
using JQuery’s wrapper around AJAX - a far simpler way than the standard
Javascript method, to the “ConfigServlet”. This, through the interface to the
simulation, SimulationServer, creates a simulation which is stored as an appli-
cation level variable. The purpose of the SimulationServer is twofold. Firstly
it allows an extension which distributes the simulation across various machines
(that would be specified by the user) using RMI.
2
Secondly, it means that the
only thing the web interface can do is create and run a simulation - everything
else is closed to it.
The user is then able to select the simulation they want to run. Like creation,
this request is sent to the “SimRunServlet” (again employing AJAX) where
the simulation server is requested to run the simulation of the identifier (name)
2
This was attempted at the beginning of the project, but difficulties with Tomcat’s security
set up caused problems with the RMI Security Manager when it came to loading Python
scripts. It was abandoned due to time constraints and the subsequent hindrance that this
caused with respect to the progression of the project. However, I believe it would be a
computationally useful extension to add if any further work were to be done on the project.
For this reason the architecture was left in place.
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Figure 9.8: Partial Screen shot showing form validation via alerts
specified. Due to the request response architecture, and the time out on requests,
the run servlet cannot be trusted to return the output of the simulation. For
this reason, the servlet executes run and then the page polls the simulation
every 10 seconds to see if it has completed. On receiving an all clear from
the PollSimulationServlet, the page then allows the simulation to be saved (the
button for saving a simulation appears). When the user clicks this button, a
request is sent to the server to generate a PDF document for download.
9.6 Distributing Simulations
As mentioned, the implementation of distributing simulations using RMI was
abandoned early on, due to the difficulties in getting around Tomcat’s Security
Manager. However, upon beginning the evaluation, it was clear that distribution
was imperative in order to complete the simulations necessary. Therefore, a
different way to achieve this was sought.
A web server called Jetty that provides an http server and client as well
as a servlet container was utilised. This allowed Tomcat to be abandoned and
replaced with Jetty. In order to distribute simulations across machines, a simple
script was created that would use ssh to remote login into a machine, execute
the war file and open Firefox. In this way, a list of machines was provided, and
simulations could be run on each of them. I also extended the servlet that runs
the simulations to run them in bulk - allowing the user to create several, and
then run them sequentially.
The result was an considerably quicker collection of results and a useful
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Figure 9.9: Illustration of process for using application
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feature for a user who wishes to run simulations in bulk, yet quickly.
9.7 Software Development Process & Testing
The software development process followed was the iterative method. This
seemed to be the most sensible option since the project was focussed on adding
multiple extensions to an initial model. The core of the simulation - the initial
model - was implemented first and thoroughly tested. Upon completion, the
next extension was tackled, and again thoroughly tested. For every extension,
the extension was designed, the model was enhanced, the interface was updated
to allow for the extra configuration, and the analysis engine was updated to
create graphs and tables specific to the extension.
This was not only a logical break down of the project, but also allowed
for changes to extensions, for new ideas to materialise, and for the direction
of the project to be steered based on how the simulations are running. In
addition it meant that extensions could remain “fuzzy” until they came to being
implemented, when the idea was researched, planned and evolved until it was
ready to be integrated in to the simulation.
The act of testing however was extremely difficult due to the inherent non-
determinism in multi-agent systems. Therefore it was imperative to exhaustively
test incrementally as an extension was added in order to be certain that I was
adding to a solid base. At the beginning it was possible to use JUnit in some
circumstances, for instance checking that the assignment of crossover agents
was being performed correctly and so on. JUnit could also be used to check
the output data for undeniably incorrect evolution of the simulation, such as
negative stocks of goods recorded. JUnit was possible for testing the setup and
outcome of the simulation, but after this point, the non-determinism made its
usefulness deteriorate. Extensive graphing of particular data (even if it was not
useful in analysis of results), for instance checking that agents who were con-
suming always exited the economy if they didn’t consume the baseline amount,
was necessary as a fallback technique to counteract this flaw. In addition, when
problems were found, the extensive eclipse debugger was used in order to iso-
late the source of the problem, and generally speaking the error could be found
through manual code inspection.
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Chapter 10
Conclusion and Further
Work
In this chapter both successes and limitations of the model will be discussed, as
well as an evaluation of implementation.
10.1 The Model
Basing the model on Wilhite’s implementation had both advantages and disad-
vantages. The decision to base it on Pareto’s idea of Pareto Superior trading
was a sensible and rational application. It is realistic since in the world of
business nobody ever makes decisions that could possibly make them worse off
knowingly.
Specialisation was witnessed in all simulations, and as division of labour
was enforced through restricting the number of agents who could produce both
goods, agents experienced strategy shifts. More agents specialised in the two
extreme ends of the continuum, becoming pure producers and pure traders and
enhancing the credibility of the simulation. It meant that increasingly more
agents could rely on the demand of the rest of the population, and, in addition,
that trade was increased through the exploiting the symmetry of the Cobb-
Douglas utility function, requiring agents to both increase and even out their
stockpiles of goods..
The evolution of the simulation showed a strong correlation between pro-
duction functions and an ability to generate wealth. This created a world in
which producers were extremely wealthy. In addition, it was not the case that
poor production in one of the goods was a disadvantage - on the contrary, as
the percentage of agents able to produce both goods fell, this position became
more advantageous. Producers could rely on demand from other agents in order
to generate wealth. This meant that in one iteration, producers could engage in
free exchange - exchange that they did not initiate - which led to the emergence
of wealth condensation. This is an extremely realistic finding - those with money
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or expertise are in a position to attract more wealth. The act of traders sacrific-
ing their goods to the producers widened the gap in wealth globally, resulting in
an increase in the Gini Coefficient. The Gini Coefficient became more realistic
with a decrease in the number of agents being able to produce both goods. This
is an emergent characteristic since initial endowments, together with production
functions, are randomly and, most importantly, uniformly distributed across the
population.
The implementation of memory showed how permitting agents to remember
encounters could both increase the loyalty of agents and cause the population
to incur strategy shifts. Thresholds were appparent as the tensions between
increased competition in the market place stemming from increasing the sight
of agents and their being able to search through their memory took their toll. It
led to loyalty for agents with memory enabled being overtaken by loyalty in the
simulation without memory enabled. Despite the ability of agents to learn and
form long-lasting trade relationships, the problem of the changing stockpiles of
agents causing memory items to be outdated would be an interesting aspect
to address. By implementing a form of garbage collection, where an agent can
periodically remove contacts from their memory in order to reduce wasted space,
this limitation could be bypassed.
Consumption further emphasised the difficult situation of traders in the new
world where bankruptcy was possible. Producers were largely unaffected by this
extension, but wealth distribution was increased considerably when constants
were set to values which limit the amount of bankruptcy, allowing agents to sur-
vive on the edge. Bankruptcy being so common, however, is not an unrealistic
thought in a model where borrowing isn’t permitted. Virtually all businesses
need loans to start up and in addition the large majority of families in the de-
veloped world have more liabilities than assets. With no financial security in
the simulation, bankruptcy should be expected, even with low values of con-
sumption. What was less realistic was who became bankrupt - once again it is
the agents who initiated trade who drew the short straw. Their poverty in the
simulation is a setback in capturing the reality of the modern world and trade.
Trade does not imply poverty. In todays world, it is more the case that raw
materials are produced by poor countries. It is the people who ship goods from
a location where they are cheap to one where they are valued who actually make
a lot of money. Trade is a massive source of income and thus the punishment
of traders is something that must be addressed first and foremost.
By analysing the networks of districts when agents were to consume, depen-
dencies and fragility in the network were witnessed, and in the simulation it
was relatively simple to accurately predict which agents would exit the econ-
omy from only the network as data. This is an extremely exciting revelation.
The vast majority of bankruptcy prediction is done using statistical models and
neural networks. In fact, very few people have approached the problem from a
perspective of interactions and network dependencies. With work and a lot of
data, this could prove to be extremely useful in economics. Its usefulness stems
from such an abstract approach, and although with the particular simulation im-
plemented here its results aren’t highly complex, it has a great amount of scope.
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Nodes can represent anything from firms to countries, regions to industries.
To highlight the potential in this idea, it is worth giving a toy example. If
a large company A goes bankrupt, this model could allow you to anticipate
how companies who are dependent on A will cope. If a company has a low
dependency on A, it is likely its demand will be met from somewhere else,
possibly a smaller company willing to offer a good price in return for some big
buys. If, however, a company is hugely dependent on A, it is likely that they
are going to feel the brunt of the bankruptcy. If A happened to be part of an
oligopoly (an industry ruled by a few big players), it is likely that the other big
players will take on old clients of A. However, if you assessed the production
capacity of these companies, and checked that the new capacity was feasible
given the extra demand, and found that prices were likely to increase due to
little redundancy in the network, then it is likely that deals will be made to
those who offer the best price. Thus, based on the strength, capital and buying
power of the dependents in the network, which can be modelled by extending
the network to be a level deeper, including who the dependents supply to, it
is possible to anticipate which companies will get the deals and which won’t.
Thus it may be possible to anticipate bankruptcies further down the chain.
However, there is another and perhaps more interesting side to this coin.
If you can make a reasonable guess as to who is going to go bankrupt, then
supply to their clients must be picked up by someone, just as was so for the
initial bankrupted company. If you can assess the production capacity of firms,
perhaps you can look at who would cope best with the new load. In turn, it
could be possible to spot some good investments - companies who will be able to
handle the new load and are likely to be taking this new load on would probably
be good
Although work is clearly needed, computing power and access to necessary
data suggest that even if this is to take time and research to make accurate, it is
worth the time and research! This further highlights the importance of network
structure in the study of economics, and offers suggestion that insight can be
gained from looking at the economy from this more abstract perspective.
Upon implementing learning, we witnessed large increases of wealth, even
above that of the Global Network (ceteris paribus) illustrating the potential
benefits that can be realised through globalisation. In addition, it was suggested
that perhaps it is true that becoming more globalised makes the world as a
whole better off, but we saw only a small, almost negligible, change in wealth
distribution. In addition, questions as to whether limitations of globalisation
were implicit in its nature, or are yet to be witnessed due to the fact that we are
yet to become truly global were discussed. The model not only demonstrated
efficiency of free trade, but also gave insights into the justification of the gains of
free trade. The study into the architecture of globalisation resembled a similar
core-periphery structure to that witnessed in the worlds international trade
network, and it was suggested that the extra decentralisation observed in the
simulation could indeed stem from protectionist policies of governments. It
was also suggested that there a strong correlation between trade deficits and
the position of countries in a network, not only persistent in the results of the
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simulation, but also readily apparent in the real world, with countries of the G8
holding some of the largest deficits.
Through evaluating the evolutionary algorithm, it was clear that in spite
of extensions creating more trade, trade was still not valued. Still a world of
production rules. The following suggestion suggests some possible alterations
to the model in order to remove the utter dependency of the wealth of an agent
on their production functions.
10.2 Alterations to the Model
As mentioned, the poverty of traders is both unrealistic and hampering to the
study of networks. If some traders could enjoy wealth akin to producers, they
would make good trade partners to other poorer traders and perhaps even to
pure producers which in turn would allow for longer trade chains, as traders
could also offer good prices. However, the alteration to the model must be done
in a way that doesn’t punish pure producers for being good at what they do,
but gives pure traders potential to make money in spite of their poor production
function. This would require some sort of “reward scheme” since you could not
just give all agents who emerge to be pure traders a random advantage.
One way of facilitating this is limiting the time agents have in which they
can search the population. Perhaps one unit of time, or one iteration, could be
made up of a number of units (most likely to be the sight of an agent). An agent
could be allowed to trade until all of its “time units” have been used up. By
employing memory of agents, agents could store encounters. At the moment,
these encounters aren’t ordered, but this could be altered so they are ranked by
gain in utility and reliability measured in number of uses. This way, one unit
of time could be used up for every potential partner an agent searches through
before settling on a trade partner. This way agents could strategically search
their memory, and if they are agents who have a few suitable trade partners, or
high loyalty, they could make an educated guess at who is likely to offer them the
best deal, and go straight to this partner. This way, agents who are successful
in quickly finding trade partners are rewarded by increasing the volume of trade
they can perform in a round. This acts then as the free exchange experienced
by pure producers, but is not damaging to the wealth of the pure producers.
In fact, it could actually increase it. It is unlikely that this would benefit the
producers so much that traders are still relatively poor. There will still be
some traders who are poor as they may not have reliable trade partners and
as such may be in the same position as before, using up most of their units
in order to find a trade partner. However, it is likely that some pure traders
would gain huge benefits from this. Perhaps they can ship goods between two
agents several times in one iteration. They improve their capability in moving
large volumes. This could cause a positive feedback loop, whereby being able to
perform multiple trades in a single iteration allows larger margins to be made,
such that next iteration they are able to trade in larger quantities and thus
make an even larger margin, and so on.
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Alternatively, instead of time, a cost could be placed on distance. Perhaps
agents can spiral outwards[6] from their position in the network, searching for
a trade partner. Thus, the further out they sought, the more expensive was
the transaction cost. This transaction cost can be thought of as analogous to
shipping, and could be paid in Good 2. This would encourage trade to occur
locally, and as such may encourage longer trade chains emerging. If the trans-
action cost correlated to distance however, you may prevent some long distance
relationships emerging. To counteract this potential problem, transaction costs
could increase with distance, but decrease with the number of times you have
engaged in exchange with the same agent.
10.3 Implementation
The main issue of problems with RMI were overcome by a simple script to deploy
the application on multiple machines. However, a great extension would be the
implementation of a method to compare results of simulation. By outputting a
CSV file of simulation data, this comparison engine could load multiple simula-
tion files, and either perform averaging of the same sort of files or alternatively
perform comparison between simulations. The most important element would
be the collaboration of similar simulations into one CSV file. It would be useful
to provide a method of customizing the data pulled out of the uploaded file to
remove any redundancy.
Although the PDF files were useful and user-friendly, when it came to eval-
uation across many simulations, it proved to be both time consuming and labo-
rious. Thus to facilitate quicker and potentially more in depth evaluation, this
is a definite extension that should be made.
The trade-off between the decrease in performance of utilising Python and
the speed added in the development process proved to be a good one. Extensions
were quick and easy to implement, and the abstraction enforced by the divide
of the scripting layer from the core facilitated better design.
The overall performance proved to be linear in terms of the number of dis-
tricts, and factorial in terms of the number of agents per district. This large
increase in time as the number of agents in a district increases is not a flaw
in implementation, but implicit in the requirement of the model since every
agent must search through every other agent in order to find a trade partner.
However, these search costs can be reduced by reducing the sight of agents.
10.4 Concluding Thoughts
In conclusion, the simulation proved that with such a simple model, complex
network structures can emerge that are easily likened to the real world. In ad-
dition, economic phenomena were witnessed, such as creative destruction and
wealth condensation, and arguments for how they occur were presented and dis-
cussed. Agents were seen to specialise, and the extensions led to some interesting
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strategy shifts. Consumption, although offering insight in to the importance of
network structure, redundancy and bankruptcy chains, was nonetheless a fairly
unstable extension. There was a fine line between catastrophic bankruptcies
and normal running of the simulation. However, a more realistic logarithmic in-
crease in wealth was witnessed which was an improvement from the linear trend.
Neoclassical economics was questioned, as prices never settled to uniform price,
despite utilising the Cobb-Douglas utility function and model of Pareto supe-
rior trading, both of which have deep roots in Neoclassical economics. The
production and consumption of goods caused price fluctuations, presenting a
simulation more akin to an open system - with matter or products, being both
created and used - as opposed to a closed static linear system.
However, the value created in the real world through moving products from
one location to another was not fully achieved. Learning most increased the
value as pure were enabled to become more strategic in their partner selection.
Despite this shortcoming, there were many successful aspects of the simulation.
In particular, the ability to produce results in the structure of the international
trade network which were so close to the real world reenforced the fact that the
simulation need not be overly complex in the way in which agents interact.
From conducting the simulations, although they lack realism in places such
as value creation from trade, it is clear that agent-based modelling is well-suited
to modelling such a complex system. Even such simplistic abstractions from
reality, such as trade of knowledge, permitted astoundingly realistic results for
the minimal level of detail employed.
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