Agent Based Computational Economics Diego Corredor Universidad Nacional de Colombia October 22, 2007

Abstract Real life economies are very complex systems composed by millions of decentralized heterogeneous agents that interact locally and give rise to global regularities such as economic growth, wealth and income distribution, labor force migration, business cycles, hyperinflation events, etc. In order to understand these complex systems, recent economic theory has tried to explain macroeconomic behavior using methodological individualism techniques. However, there are several obscure issues that make this approach a very limited tool of analysis. This fact points out that there has not been a natural approach to model highly heterogeneous agents and the interaction among them. This paper presents a new computational methodology, called Agent based Computational Economics (ACE), that studies economies as complex adaptive systems. Two “classical” ACE models are described to sketch the most important features of this methodology, as well as its strengths and weaknesses respect to traditional economic modeling.

JEL Classification: C63, D5, D7, E17

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Introduction

Real life economies are composed by millions of decentralized heterogeneous agents interacting locally, unwillingly giving rise to global regularities such as economic growth, unemployment, national savings, income distribution, etc. However these global regularities affect themselves and individual behavior simultaneously. In these sense an economic system is a dynamical entity with complex feedback and feedforward structures between decentralized individuals’ behavior, economic interaction rules and global regularities. Economic theory has focused on two major research fields, namely micro and macroeconomics, in order to understand these complex economic systems. While microeconomic theory has constructed a detailed theoretical description of individual economic units composing the system (consumers, firms, institutions, monopolies, public goods, etc.), macroeconomics have developed a strong theoretical body to understand systems’ global behavior (economic growth, inflation, business cycles and so on.). However, economic theorists have found big challenges when trying to interconnect micro and macro economic theories. These challenges relate to two different issues. First, there is no solid explanation about the way individual behavior and local interactions give rise to global regularities. Second, the way in which global regularities affect individual decisions, as well as local interaction rules, is obscure by now. These issues result very hard to handle because agent’s decentralized interactions, and the complex feedback structure among them, make economic systems to observe nontrivial dynamics, emergent properties, strong correlation or, what it is usually called, complex behavior. Because of these properties of economic systems, theorists are required to make strong simplifying assumptions in order to derive analytical tractable models. From these analytical, relatively simple models, some very important lessons have been learnt; but, because of its own simple nature, models’ insights are extremely constrained results which may be of little help if the economic phenomenon under study possesses a highly complex behavior. On the other hand, when more realistic assumptions are taken into account, models become highly complex and impossible to solve analytically. The only way to solve this kind of “more realistic” models is to make assumptions on functional forms and use computer simulation techniques. Again, models insights are constrained, this time by functional forms and parameter

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value assumptions. However, the use of simulation makes it possible to evaluate the effects of functional and parameter assumptions on final results. This paper presents a new computational approach dealing with economic complexity, called Agent Based Computational Economics (ACE). Because it is a relatively new approach, the paper sketches its most important features, as well as its strengths and weaknesses. In order to point out some of its specific advantages and disadvantages to traditional modeling, two ACE “traditional” models are presented. This paper contains 4 sections, including this introduction. Next section describes some of the most important features of ACE methodology. Section 3 presents several advantages and disadvantages of Agent Based Computational Economics. Finally, section 5 concludes.

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ACE Methodology

If one should survey last twenty years of economic theoretical advancements one would surely find representative agent assumption very often. Unfortunately in most cases this assumption is made not because researchers think it is realistic, but because there has not been a truly workable methodology to deal with heterogeneity1 . Although there exists wide economic literature dealing with heterogeneous agents models2 , there is a part of picture that has been missing because the representative agent assumption abstracts two different economic features: 1) Agents’ physical, psychologic and economic heterogeneity; and 2) the way in which these agents interact3 . The first point is obvious and has been studied by the literature cited above. However, once heterogeneity has been put into account, it must be specified how the heterogeneous agents interact. In traditional heterogeneous modeling it is common practice to assume that aggregate behavior is just the sum and/or the average of individuals’ behavior. However there is no argument to justify this. For example, aggregate savings is clearly the sum of individuals’ savings levels. But when analyzing the effect of a simple interest rate change, aggregate savings movement is the result of many different individual responses to this shock, and there is no particular reason to expect it to be the 1

(Axtell and Epstein 1996, p. 2) See (Heer and Maussner 2005, part II). 3 (Kirman 1992) 2

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average movement in individual savings levels. In other words, when considering heterogenous agents, it is possible to observe that the aggregate is more, or even less, than the sum or the average of its parts4 . Agent Based Computational Economics (ACE) is a new methodology for the study of economies as complex adaptive systems. It allows to model heterogenous adaptive agents who interact using different interaction rules simultaneously. The methodology does not make oversimplifying assumptions to get analytical tractable models. That is why ACE models tend to have an intricate structure, because they can simultaneously deal with bounded rationality, incomplete information, incomplete markets, and other “less abstract” (“more realistic”?) assumptions. It could be argued that some traditional models do also focus on agents heterogeneity. However compared to traditional approaches, ACE methodology does not impose market clearing conditions, or any other aggregate behavior constraints. It is concerned primarily with the way heterogeneous individual preferences give rise to particular aggregate behaviors. Following Testfatsion’s words: One principal concern of ACE researchers is to understand why certain global regularities have been observed to evolve and persist in decentralized market economies despite the absence of top-down planning and control[...] A second principal concern of ACE researchers is to use ACE frameworks normatively, as computational laboratories within which alternative socioeconomic structures can be studied and tested with regard to their effects on individual behavior, interaction networks, and social welfare5 . Another big departure of ACE models from traditional ones is that there is no particular interest on market clearing equilibrium situations. Most of the analysis has to do with disequilibrium and the way dynamic properties of the economic system let this situation evolve over time. Even more, because of this reduced interest on market clearing equilibrium, there 4

This is called an emergent property of the system, and it is one of the most important features in complex

systems literature (Bruun 2005). 5 (Testfatsion 2001, p. 1).

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can exist several equilibrium conceptions for a particular model. For example, in Testfatsion’s Trading World model6 some possible equilibrium situations are when: 1. The economy exhibits an unchanging carrying capacity, in the sense that it supports an unchanged number of solvent firms and viable consumers over time. 2. The economy exhibits continual market clearing, in the sense that demand equals supply in all markets over time. 3. The economy exhibits an unchanging structure, in the sense that the capacity levels (hence fixed costs) of the firms are not changing over time. 4. The economy exhibits and unchanging trade network, in the sense that who is trading with whom, and with what regularity, is not changing over time. 5. The economy exhibits a steady-state growth path, in the sense that the capacities and production levels of the firms and the consumption levels of the consumers are growing at constant rates over time. And these are just some of the possible equilibrium conceptions for that particular model. Depending on what particular issue is being analyzed, the ACE researcher can determine what particular conception is best to consider. So ACE researchers do not deny or de-estimate the existence of equilibria, whatever the criteria is. In fact, in any ACE model there must always be some equilibrium conception. But the ACE researcher is aware that equilibria are very particular situations that must be characterized and understood in order to have a reference point, but he/she also knows that the most interesting analysis is about what happens when the system is out of equilibrium7 . Another difference of ACE models is that there is a true economic interaction among agents. Contrary to general equilibrium and game theory models, ACE methodology does not impose specific interactions constraints (for example Walrasian Auctioneer, or predetermined strategic interaction) nor market clearing conditions, or any other aggregate behavior constraint. Agents interact freely following particular rules that guide their behavior but do not centralize interaction nor determine whom to interact with. 6 7

(Testfatsion 2006). (Arthur ).

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Finally, ACE models do not need any exogenous shock for keep on moving. This feature is not strange when models’ complex feedback structure and agents’ adaptive behavior are taken into account. It was already said that agents’ decisions and interactions determine global regularities and their behavior, but these regularities also affect the way agents act and/or interact. The result then is a highly complex, usually analytical intractable, dynamic adaptive system that can only be studied through computater simulation.

2.1

Model Structure

Although ACE models observe very complex behavior, they are very simple in structure. In general, any model can be viewed as a set of agents that follow some interaction rules within a particular environment. These are the three fundamental components of any ACE model8 : 2.1.1

Agents

Each agent has internal states and behavioral rules. For example: age, preferences, sex, expectatives formation rules, metabolism rate, wealth, cultural identity, health, etc. Some of these will be fixed during agent’s life, but there are others that may change/evolve through interaction. As it will be discussed later, this wide range of possible internal states and behavioral rules is one of the strengths and weaknesses of ACE methodology. 2.1.2

Environment

“The environment is a medium separate from the agents, on which the agents operate and with which they interact”9 . It can be an abstract structure, like a communication network, or a spacial object with given dimensions, like the Sugarscape presented below. Like agents, the environment has internal states and behavioral rules that can either be fixed or change over time. For example: topography, resource holdings, communication nodes, etc. 8 9

This subsection is based on (Axtell and Epstein 1996, ch. 1) (Axtell and Epstein 1996, p. 5).

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2.1.3

Interaction Rules

The key departure from traditional heterogeneous agents models is the interaction structure considered. Within any ACE model there can exist three different types of rules: agent environment, environment - environment and agent - agent rules. Each one governs and guides the interaction among the different components of the model.

2.2

Some Examples

In order to exemplify some of the features already mentioned and to prepare the ground for the explanation of the advantages and disadvantages of using ACE models, in what follows two “classical” ACE models are presented. 2.2.1

Neighborhood Segregation Model

This model is one of the pioneer works in agent based computational economics. It was developed by Thomas Schelling in the 1970’s10 . Although it is not an economic model, it is very important in ACE literature because it is the first model that explicitly studies how micro-level preferences manifest themselves at the macro-level. As Schelling comments:

“[...]processes of separation, segregation, sharing, mixing, dispersal have a feature in common. The consequences are aggregate but the decisions are exceedingly individual[. . . ] The results can be unintended, even unnoticed.”11 In short, the segregation model works as follows:

There is a certain number of agents inhabiting a neighborhood composed by a given number of squares. Each square can be inhabited by no more than one agent12 . Agents are supposed to be members of two different groups, reds and whites. Each agent demands a minimum number of same colored agents living next to him. If the number of opposite color agents living next to the agent exceeds its demand, then the agent moves to the nearest empty square satisfying its demands. 10

See (Schelling 1978). (Schelling 1978, p.145). 12 It is assumed that the number of squares is greater than the number of inhabitants. 11

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With this simple model Schelling tried to answer some very interesting questions like: What is the connection between individual prejudice and observed patterns of spacial segregation? Is it possible to get highly segregated settlement patterns even if most individuals are color-blind?

The key components of this model are described below: Agents As it was already said, there exist two homogeneous populations of agents, each one being identified by a given color (red or white). Each individual demands his own neighborhood being populated by at least a given number of same colored agents. If the individual preference for like-colored neighbors is not satisfied, then the agent moves to another empty square satisfying her demand.

Environment Agents interact on a bidimensional lattice denominated neighborhood. Each square in the neighborhood can be inhabited by no more than one agent. The eight squares surrounding an agent are denominated agent’s own neighborhood or local neighborhood 13 .

Interaction Rules There is only one interaction rule in the model. This is an agent - agent rule and it can be stated as follows14 : Agent Movement Rule: 1. The agent computes the fraction of neighbors who are its own color; 2. If this number is greater than or equal to its preference, the agent is considered satisfied, in which case end, else continue; 3. The agent looks for the nearest unoccupied lattice site that satisfies its preference and moves there. 13 14

These eight squares are denominated Moore Neighborhood. See (Axtell and Epstein 1996, p. 37). Taken from (Axtell and Epstein 1996, p. 165).

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This rule is applied sequentially (starting from the upper left corner and finishing in the lower right one) to each living agent in the neighborhood. After all agents have been updated, next time period begins and the rule is applied again.

Simulation It is assumed that there are 2.000 individuals randomly placed in a bidimensional neighborhood of 50 × 50 squares. There is always equal number of red and white - colored agents. Empty sites are black-colored squares. In order to observe the way segregation patterns arise due to changes in individual preferences, the parameter demand for like-colored neighbors is modified. Note that random distribution of agents does not necessarily generate an equilibrium situation (i.e. a situation where all agents are satisfied, and no one wants to move). It is also worth noting that, although the first individual (upper left corner) would be satisfied right after the movement rule has been applied to him, it does not assure that he will satisfied at the end of the time period because other agents decisions may modify his local neighborhood: “Anybody who moves leaves a blank cell that somebody can move into. Also, anybody who moves leaves behind a neighbor or two of his own color; and when he leaves a neighbor, his neighbor loses a neighbor and may become discontent. Anyone who moves gains neighbors like himself, adding a neighbor like them to their neighborhood but also adding one of opposite color to the unlike neighbors he acquires”15 This is a truly decentralized behavior and the quotation gives an idea about the difficulty to predict how agent’s location would be after all individuals have been updated. But before running the simulation, one could make the following unwary analysis. It would seem reasonable to assume that the less tolerant the agents are to unlike-colored neighbors, there would be more likely individuals willing to move to like-colored concentrated areas. It means that one should be expecting to observe more segregated outcomes when agents are less tolerant. 15

(Schelling 1978, p. 150).

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Figure 1: At least 20 % of Like - Colored Neighbors

Figure 2: At least 40 % of Like - Colored Neighbors

Figures 1, 2 and 3 present system’s evolution for three different tolerance values16 . Left hand panels present initial conditions of the squared neighborhood (using an uniform random distribution), while right hand panels show system’s state after 20 time periods. As the analysis made above predicts, Figure 1 shows that for a huge toleran society segregation is almost non-existent. Right panel in this figure observes some particular regions where red individuals concentrate, however this concentration is not so strong. Figure 2 is more unexpected. Although intuition is correct in that there would be a more segregated outcome than that presented in Figure 1, the right panel shows that, even when agents are willing to tolerate more than 50% of their neighbors to be of the opposite colors, a highly segregated situation is obtained. 16

This figures have been taken from (Gonz´ alez 2004).

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Figure 3: At least 90 % of Like - Colored Neighbors

But the more striking result is that presented in Figure 3. The brief analysis made above would say that this should be the more segregated outcome of those presented here. Nonetheless, this is just the opposite. The right panel shows that there is no clearly segregated areas. What is happening then? What is wrong with the analysis made before? The left panel in figure 3 shows that, because of the random allocation, almost all individuals want to move to better squares. But this movement generates unexpected changes in other agents’ own neighborhoods that can made them unsatisfied. So at the end of the first time period, there may be still many unsatisfied individuals willing to move. In the next period, those unsatisfied agents will move to better squares, leaving behind discontent neighbors. The result is that at the end of each period there would be again a great number of unsatisfied individuals. A closer dynamical look to the simulation would show that while the first two situations lead to equilibrium situations17 , in the last artificial society there will always be discontent individuals willing to move at each time period. What failed in the first analysis was the assumption that more segregated individual preferences will produce a more segregated aggregate outcome. In other words, it was wrongly assumed that the aggregate outcome was the aggregation of individual behaviors. 17

Meaning by equilibrium that all agents are satisfied and nobody wants to move.

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2.2.2

SugarScape Model

The second model reviewed here is the Sugarscape Model. It was developed at the Santa Fe Institute by Joshua Epstein and Robert Axtell in the early 1990’s to study trade, migration, group formation, combat, transmission of culture, propagation of disease and population dynamics. This makes the model to observe highly complex structure18 . The model works as follows: There exists a landscape (squared lattice) populated by a given number of agents. This landscape is a topography of a renewable resource (sugar) that agents must eat to survive. Individuals are characterized by their metabolism and their vision capacity. At each time, agents look for the nearest site with highest resource holdings and move there. Every time an agent moves, a given amount of her sugar holdings is “burned”. Finally, agents die if they do not have enough sugar to move. This model differs from Schelling’s in that the environment is more than just a spacial structure. It becomes a communication network among agents. In this sense, the environment plays a more active role, as it is described as follows19 .

Environment As it was mentioned above, the environment is a squared lattice with a spacial distribution of a renewable resource (“sugar”). Each site in the lattice has a sugar level and a sugar capacity (maximum level of sugar level). This allows the possibility to find some points with zero sugar level while others might be rich in sugar. In particular, sugar is distributed such that the northeast and the southwest quadrants of the grid have the highest levels of sugar. Figure 4 shows this fact, yellow areas are sugar richest squares while black areas have zero sugar level. The red dots in the lattice represent the living agents. The environment plays a more important role in this model because the sugar distribution makes agent’s spacial location a very important feature of heterogeneity. If an agent is located 18

The simplest version of the model is described here. For further information on more elaborated versions

of the Sugarscape model see (Axtell and Epstein 1996). 19 This part is based on (Axtell and Epstein 1996, Ch. 2).

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Figure 4: A Sugarscape in low sugar areas, it is highly probable she will have low sugar holdings. However, if a given agent is located in a high sugar level area, she will have a higher survival probability. In other words, the environment will affect agents’ performance.

Agents Each agent is characterized by four state variables. In first place, one state of the agent is her location on the sugarscape. This is what Axtell and Epstein call agent’s “environmental endowment”. The spacial distribution can follow a random process or an arbitrary rule. The second and third state variables are called “genetic endowment” because they have to do with agent’s metabolism and vision capacity. By metabolism is understood the amount of sugar burned by the agent per time step, or iteration. The vision variable determines the number of sites ahead the agent can inspect in her food search20 . Both of these variables are randomly distributed across agents, giving rise to agent heterogeneity. The last state variable is agent’s wealth or sugar holdings. This is determined by the collected, but not eaten, sugar. It is assumed that agents’ holdings do not decay over time, except because of metabolism. If at any time, agent’s wealth falls to zero or below, then it is said that the agent has starved to death and she is removed from the model.

Interaction Rules 20

In order to introduce some type of imperfect information, it is assumed that agents are diagonal blind. It

means that agents can only see in the four principal directions: north, south, east and west.

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In this case there are two rules, the environment growth back rule and the agent movement rule. Agent Movement Rule:21 1. Look out as far as vision permits in the four principal lattice directions and identify the unoccupied site(s) having most sugar22 ; 2. If the greatest sugar value appears on multiple sites then select the nearest one; 3. Move to this site; 4. Collect all the sugar at this new position. In order to elude any asymmetry, the agent movement rule is applied randomly to all living agents in the sugarscape. Sugarscape Growback Rule:23 Once a given agent has eaten all sugar in a particular site, there can be several “grow back rules”: • Sugar could grow instantly to its capacity, or • Sugar could grow back at different rates in different regions over the sugarscape, or • The grow back rate might depend on the sugar level of neighboring sites. One could think in many other grow back rules. However, it is often recommended to use as simple rules as possible in order to identify key results emerging from them.

Simulation The simulation exercise considers a 50×50 squared sugarscape like the presented in Figure 4. Over the squared lattice there are 400 randomly distributed agents with uniformly distributed vision (between 1 and 6 squares) and metabolism (between 1 and 4 sugar units). The maximum 21

See (Axtell and Epstein 1996, p. 25). The order in which each agent searches the four directions is random. 23 See (Axtell and Epstein 1996, p. 23). 22

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a. Iteration 5

b. Iteration 10

c. Iteration 20

d. Iteration 2.000

Figure 5: Spacial Location over Time sugar capacity is 4 (yellow sites) and the minimum is 0 (black areas). Finally, it is assumed that sugar level grows back 1 unit per iteration until sugar capacity is reached. Given the interaction rules, it is expected that there will not be an equilibrium situation as the observed in the Schelling model, namely that no-agent wants to move. In fact, agents will always keep moving, except when their sugar holdings fall to zero. In this sense, it is more interesting to analyze different aspects such as sugar wealth distribution, number of survivors over time and the characteristics of these survivors. Figure 5 presents the evolution of the sugarscape over time. It can be observed that those agents located deep in zero sugar areas (black zones) are condemned to starvation, while luckier individuals migrate to higher level sugar areas. As panel d. shows, the survivor agents agglomerate around the northeast and southwest quadrants. This fact also determines the way wealth distribution evolves over time. Figure 6 shows that in the first periods wealth distribution is 15

a. Iteration 1

b. Iteration 500

c. Iteration 1.000

d. Iteration 2.000

Figure 6: Wealth Distribution over Time concentrated in low sugar holdings. As agents migrate to high sugar level areas, the wealth distribution moves to the right. However, just after 4.000 iterations it is possible to observe a relatively equal distribution among agents. It means that inequality is an emerging property of this system, and it is definitively related to the environmental and genetic endowments. Figure 7 presents two interesting results. The left hand panel shows that population decreases rapidly during the first periods. This occurs because agents located in black areas starve to dead. However, after the starvation of the unlucky, the population continues decreasing (although at lower speed). This process can be explained by taking a look to the right hand panel. It can be observed that the average vision augments over time, while average metabolism decreases. What it is happening here is a natural selection. Individuals better suited (with high vision and low metabolism) survive while less suited agents die. The results of these two models show a very important feature of ACE models, namely that the aggregate behavior can be more (or even less) than the sum of its parts. And this is directly connected with the so called emergent properties, or properties of the system that were not stated in the interaction rules but which are inexorably a consequence of them. Next section 16

Figure 7: Population and Average Attributes over Time is devoted to point out more specific advantages and disadvantages of using ACE models in economics.

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Advantages and Disadvantages

When some new methodology is proposed it is worth to identify the pros and cons of using it respect to traditional methodologies; this section is devoted to present more specific advantages and disadvantages of the Agent Based Computational Economics approach24 .

3.1

Strengths

It is possible to consider several aggregation levels simultaneously and in a natural way Any society is composed by agents. However, these agents often conform more complex units like families, firms, neighborhoods, private institutions, production sectors, and so on. These are intermediate aggregation levels between single agents and global regularities. Beliefs, preferences, behavior patterns and interaction rules can be set to change endogenously over time Agents’ internal states and behavioral rules can be set to change through interaction. This gives ACE models a more dynamical nature than traditional recursive dynamics, and this is 24

It should be clear that the objective of this section is not to argue that traditional models are not useful. In-

deed, traditional economic research and ACE methodology have complementary agendas rather than competing ones.

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primarily a consequence of treating the time variable as historic rather than logic25 . Agents’ rationality level can be bounded relatively easy Any ACE model handles a huge amount of data each run, and agents can be easily restricted about the way this information is processed. It can lead to simultaneous levels of bounded rationality within agents. Access to information can be restricted at different levels for different individuals Because each agent is treated as an individual software entity, model programming requires to specify what information is shared between different interacting units. This makes easy to introduce asymmetric information to agents interaction process26 . Even more, it is possible to change asymmetric information patterns over time. Agents’ heterogeneity is almost immediate, and it is broader than traditional modeling has considered Once agents’ internal states, and behavioral rules, are allowed to change over time, and different levels of information access are allowed to coexist, agents’ heterogeneity is not a problem anymore. Even more, it becomes a natural way of thinking. Interaction patterns are characterized by communication networks, spacial location or both. Interaction patterns can be characterized by spacial placement (like in the Neighborhood Segregation Model), abstract structures, or both (like in the Sugarscape model). This allows the ACE researcher to associate certain interaction patterns with particular spacial and/or communication properties. 25 26

See . See footnote 20.

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There are no messy problems of missing data or uncontrolled variables as there are in experimental or observational studies It is possible for the ACE researcher to get almost any specific information. It can happen that after analyzing some results, it is desirable to study some unreported data. In traditional experimental or observational studies this would be a major problem. However, in ACE models it can be done by extracting the desired data and running the model again. Complete description of structural attributes, institutional arrangements and agents’ behavioral rules As it was said before, ACE researchers are specially interested in understanding how global regularities arise. In order to reach this goal, it is important to make a complete description of system’s components, and the way they are related to each other, in order to describe the most important transmission channels from individual behavior to global regularities. This fact assures that the ACE researcher is more aware about all the behavioral and institutional assumptions that she has made during all the modeling process. Programming is simpler and more intuitive than other computational approaches ACE models are often implemented using Object Oriented Programming (OOP). Respect to traditional model implementations, OOP a is more intuitive approach because each agent composing the system is implemented as a single software object with some given properties and some particular actions to perform. Finally, using the OOP it is posible to increase very easily the number of agents, and other different attributes, with no significative coding change. ACE models can be set to replicate traditional ones Because of the ability to model a wide range of heterogeneity, ACE methodology is able to model a particular situation where all agents are similar to each other (this is the representative agent assumption). If all agents, interaction rules, and the environment specification, are similar to a traditional model, then the ACE model should replicate its results. It means that agent based computational models can be “calibrated ” to obtain standard results.

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3.2

Weaknesses

Multiple runs are required Each model run presents sufficient conditions to obtain a given behavior (specific parameter values, particular interaction rules, initial conditions and so on.). For example, let suppose that for some particular parameter values a given ACE model generates cyclical behavior. The model run then would give sufficient conditions to obtain cyclical behavior. However, it cannot be stated that cyclical behavior is a global feature in the model. There must be ran a great number of model runs in order to have some idea on the stability of the cyclical result. Complete description of structural attributes, institutional arrangements and agents’ behavioral rules It was already argued that the complete description of structural attributes is a strength. Nonetheless, it can also be a threat to ACE modeling since this complete description requires to make several behavioral and institutional assumptions. If the ACE researcher is very careful in doing such assumptions, then it would be a strength. But if those assumptions are made in an irresponsible manner, then any simulation exercise will have no sense. Resulting series could be chaotic Because of the nonlinear nature of ACE models, the resulting series obtained from model runs can be chaotic. It means that a small change in model’s initial conditions can conduce to very different quantitative results. This can be a big problem when parameter approximation is made. To overcome this difficulty ACE researchers must check the stability of results through sensitivity analysis. As in most young fields, the promise is greater than proven accomplishments27 ACE methodology is a very young field of research. Although at first hand it could seem to be a very fertile research area, only a closer look will show how powerful this new methodology really is. 27

(Axelrod 2003, p. 1)

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Concluding Remarks

This paper introduced the Agent Based Computational Economics methodology as a new approach to study complex adaptive economic systems. It differs from other methodologies in what it allows the researcher to consider less restricted scenarios where heterogenous evolving agents, bounded rationality, incomplete information, etc., play an important role. However, because of the relaxation of traditional assumptions, ACE models have a very complex structure that: 1) make necessary several model runs; and 2) can give rise to chaotic results. In conclusion, ACE modeling, as a very young field of research, has some advantages respect to traditional economic modeling. However, “as in most young fields, the promise is greater than proven accomplishments”27 , it is necessary a closer look to determine if its advantages are bigger than the disadvantages.

References Arthur, W.B. Chapter Out-of-Equilibrium Economics and Agent-Based Modeling of Handbook of Computational Economics, Vol 2: Agent-Based Computational Economics, edited by Leigh Testfatsion and Kenneth L. Judd. ELSEVIER/North-Holland, Amsterdam, the Netherlands. Auayang, S.Y. 1999. “Synthetic Analysis of Complex Systems I - Theories.” Mimeo. Axelrod, R. 2003. “Advancing the Art of Simulation in the Social Sciences.” Japanese Journal for Managment Information System 12, no. 3. Axelrod, R., and L. Testfatsion. 2006. Chapter Apendix: A Guide for Newcomers to AgentBased Modeling in the Social Sciences of Handbook of Computational Economics, Vol 2: Agent-Based Computational Economics, edited by Leigh Testfatsion and Kenneth L. Judd. ELSEVIER/North-Holland, Amsterdam, the Netherlands. Axtell, R. 2000. “Why agents? On the Varied Motivations for Agent Computing in the Social Sciences.” Working Papers, Center on Social and Economic Dynamics, no. 17. Axtell, R., and J.M. Epstein. 1996. Growing Artificial Societies: Social Sciencie from the Bottom Up. Brookings Intittution Press, Washington, D.C.

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Bruun, C. 2005. “Agent-Based Computational Economics - An Introduction.” Mimeo. Gardner, M. 1970. “Mathematical Games: The Fantastic Combinations of John Conway’s New Solitaire Game “life ”.” Scientific American 223 (October): 120–123. Gilbert, N. 1996. Chapter Holism, Individualism and Emergent Properties: An Approach from the Perspective of Simulation of Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View, edited by Hegselmann et al. Dordrecht Kluwer. Goldspink, C. 2002. “Methodological Implications of Complex Systems Approaches to Sociality: Simulation as a Foundation for Knowledge.” Journal of Artificial Societies and Social Simulations 5, no. 1. http://www.soc.surrey.ac.uk/JASSS/5/1/3.html. Gonz´alez, S. 2004. “¿Sociedades Artificiales? Una Introducci´on a la Simulaci´on Social.” Revista Internacional de Sociolog´ıa, no. 39:199–222. Heer, B., and A. Maussner. 2005. Dynamic General Equilibrium Modelling. Springer. Kirman, A. 1992. “Whom or What Does the Representative Individual Represent?” Journal of Economic Perspectives 6 (2): 117–136. LeBaron, B. 2002. “Building the Santa Fe Artificial Stock Market.” Brandeis University, Mimeo. Marney, J.P., and H.F. Tabert. 2000. “Why do simulation? Towards a Working Epistemology for Practitioners of the Dark Arts.” Journal of Artificial Societies and Social Simulation 3, no. 4. http://www.soc.surrey.ac.uk/JASSS/3/4/4.html. Schelling, T.C. 1978. Micromotives and Macrobehavior. W.W. Norton & Company, New York. Terna, P.

1998.

“Simulation Tools for Social Scientists: Building Agent Based Mod-

els with SWARM.”

Journal of Artificial Societies and Social Simulation 1, no. 2.

http://www.soc.surrey.ac.uk/JASSS/1/2/4.html. Testfatsion, L. 2000. “Agent-Based Computational Economics: A Brief Guide to the Literature.” Mimeo. . 2001. “Guest Editorial: Agent-Based Modelling of Evolutionary Economic Systems.” IEEE Transactions on Evolutionary Computation 5, no. 5.

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. 2006. Chapter Agent-Based Computational Economics: A Constructive Approach to Economic Theory of Handbook of Computational Economics, Vol 2: Agent-Based Computational Economics, edited by Leigh Testfatsion and Kenneth L. Judd. North-Holland, Amsterdam, the Netherlands. Vicsek, T. 2002. “Complexity: The Bigger Picture.” Nature 418 (July): 131.

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