Complexity hints for economic policy

New Economic Windows

Series Editor

MASSIMO SALZANO

Series Editorial Board

Jaime Gil Aluja

Departament d’Economia i Organització d’Empreses, Universitat de Barcelona, Spain

Fortunato Arecchi

Dipartimento di Fisica, Università di Firenze and INOA, Italy

David Colander

Department of Economics, Middlebury College, Middlebury, VT, USA

Richard H. Day

Department of Economics, University of Southern California, Los Angeles, USA

Mauro Gallegati

Dipartimento di Economia, Università di Ancona, Italy

Steve Keen

School of Economics and Finance, University of Western Sydney, Australia

Giulia Iori

Department of Mathematics, King’s College, London, UK

Alan Kirman

GREQAM/EHESS, Université d’Aix-Marseille III, France

Marji Lines

Dipartimento di Science Statistiche, Università di Udine, Italy

Alfredo Medio

Dipartimento di Scienze Statistiche, Università di Udine, Italy

Paul Ormerod

Directors of Environment Business-Volterra Consulting, London, UK

J. Barkley Rosser

Department of Economics, James Madison University, Harrisonburg, VA, USA

Sorin Solomon

Racah Institute of Physics, The Hebrew University of Jerusalem, Israel

Kumaraswamy (Vela) Velupillai

Department of Economics, National University of Ireland, Ireland

Nicolas Vriend

Department of Economics, Queen Mary University of London, UK

Lotfi Zadeh

Computer Science Division, University of California Berkeley, USA

Editorial Assistants

Maria Rosaria Alfano

Marisa Faggini

Dipartimento di Scienze Economiche e Statistiche, Università di Salerno, Italy

Marisa Faggini

Dipartimento di Scienze Economiche e Statistiche, Università di Salerno, Italy

Series Editorial Board

Jaime Gil Aluja

Departament d’Economia i Organització d’Empreses, Universitat de Barcelona, Spain

Fortunato Arecchi

Dipartimento di Fisica, Università di Firenze and INOA, Italy

David Colander

Department of Economics, Middlebury College, Middlebury, VT, USA

Richard H. Day

Department of Economics, University of Southern California, Los Angeles, USA

Mauro Gallegati

Dipartimento di Economia, Università di Ancona, Italy

Steve Keen

School of Economics and Finance, University of Western Sydney, Australia

Alan Kirman

GREQAM/EHESS, Université d’Aix-Marseille III, France

Marji Lines

Dipartimento di Science Statistiche, Università di Udine, Italy

Thomas Lux

Department of Economics, University of Kiel, Germany

Alfredo Medio

Dipartimento di Scienze Statistiche, Università di Udine, Italy

Paul Ormerod

Directors of Environment Business-Volterra Consulting, London, UK

Peter Richmond

School of Physics, Trinity College, Dublin 2, Ireland

J. Barkley Rosser

Department of Economics, James Madison University, Harrisonburg, VA, USA

Sorin Solomon

Racah Institute of Physics, The Hebrew University of Jerusalem, Israel

Pietro Terna

Dipartimento di Scienze Economiche e Finanziarie, Università di Torino, Italy

Kumaraswamy (Vela) Velupillai

Department of Economics, National University of Ireland, Ireland

Nicolas Vriend

Department of Economics, Queen Mary University of London, UK

Lotfi Zadeh

Computer Science Division, University of California Berkeley, USA

Editorial Assistants

Marisa Faggini

Dipartimento di Scienze Economiche e Statistiche, Università di Salerno, Italy

Massimo Salzano • David Colander

Complexity Hints

for Economic Policy

MASSIMO SALZANO

Dipartimento di Scienze Economiche e Statistiche

Università degli Studi di Salerno, Italy

David Colander

Middlebury College, Middlebury, VT, USA

Library of Congress Control Number: 2006930687

ISBN-978-88-470-0533-4 Springer Milan Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole of part of the

material is concerned, specifically the rights of translation, reprinting, re-use of illustrations,

recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data￾banks. Duplication of this pubblication or parts thereof is only permitted under the provisions

of the Italian Copyright Law in its current version, and permission for use must always be

obtained from Springer-Verlag. Violations are liable for prosecution under the Italian

Copyright Law.

Springer is a part of Springer Science+Business Media

© Springer-Verlag Italia 2007

Printed in Italy

Cover design: Simona Colombo, Milano

Typeset by the authors using a Springer Macro package

Printing and binding: Grafiche Porpora, Segrate (MI)

Printed on acid-free paper

IV A. Achiron et al.

The publication of this book has been made possible thanks to the financial

support of the MIUR-FIRB RBAU01 B49F

springer.com

Preface

To do science is to find patterns, and scientists are always looking for pat￾terns that they can use to structure their thinking about the world around

them. Patterns are found in data, which is why science is inevitably a quan￾titative study. But there is a difficulty in finding stable patterns in the data

since many patterns are temporary phenomena that have occurred ran￾domly, and highly sophisticated empirical methods are necessary to distin￾guish stable patterns from temporary or random patterns.

When a scientist thinks he has found a stable pattern, he will generally

try to capture that pattern in a model or theory. A theory is essentially a

pattern, and thus theory is a central part of science. It would be nice to

have a single pattern - a unified theory - that could serve as a map relating

our understanding with the physical world around us. But the physical

world has proven far too complicated for a single map, and instead we

have had to develop smaller sub maps that relate to small areas of the

physical world around us. This multiple theory approach presents the prob￾lem of deciding not only what the appropriate map for the particular issue

is, but also of handling the map overlays where different maps relate to

overlapping areas of reality.

It is not only science that is focused on finding patterns; so too are

most individuals. In fact, as pointed out by Andy Clark (1993), human

brains are ‘associative engines’ that can be thought of as fast pattern com￾pleters - the human brain has evolved to see aspects of the physical world

and to create a pattern that places that aspect in context and allows indi￾viduals to draw broader implications for very limited data1

. Brian W. Ar￾thur gives the following example ‘If I see a tail going around a corner, and

it’s a black swishy tail, I say, “There’s a cat”! There are patterns in music,

——————

1

This discussion is based on observations by Brian W. Arthur (2000).

VI Preface

art, religion, business; indeed humans find patterns in just about everything

that they do2

.

Determining when a pattern fits, when there are multiple patterns map￾ping to the same physical phenomena, and which pattern is the appropriate

pattern, is a difficult task that is the subject of much debate. Science differ￾entiates itself from other areas of inquiry by setting rules about when a pat￾tern can be assumed to fit, and when not, and what the structure of the map

can be. It essentially is a limit on the fast pattern completion nature of hu￾mans. For example, that swishy tail could be a small boy with who is play￾ing a trick with a tail on one end of a stick.

To prevent too-fast pattern completion, and hence mistakes, standard

science requires the map to be a formal model that could be specified in a

set of equations, determined independently of the data sequence for which

it is a pattern, and that the patterns match the physical reality to a certain

degree of precision. That approach places standard logic at the center of

science. Arthur tells the story of Bertrand Russell’s to make this point. A

schoolboy, a parson, and a mathematician are crossing from England into

Scotland in a train. The schoolboy looks out and sees a black sheep and

says, ‘Oh! Look! Sheep in Scotland are black!’ The parson, who is learned,

but who represents a low level of science, says, ‘No. Strictly speaking, all

we can say is that there is one sheep in Scotland that is black’. The

mathematician, who might well represent a skilled theoretical scientist,

says, ‘No, that is still not correct. All we can really say is that we know

that in Scotland there exists at least one sheep, at least one side of which is

black’. The point is that science, and the formal models that underlie it,

works as a brake on our natural proclivity to complete patterns.

In many areas the standard science approach has served us well, and

has added enormous insight. By insisting on precision, scientists have built

an understanding that fits not just the hastily observed phenomena, but the

carefully observed phenomena, thereby developing much closer patterns.

Once individuals learn those patterns, the patterns become obvious to them

- yes, that table is actually nothing but a set of atoms - but without science,

what is obvious to us now would never have become obvious. In other ar￾eas, though, we have been unable to find a precise set of equations or

models that match the data representing the physical world, leaving large

areas of physical reality outside the realm of science. For many scientists,

——————

2

Human’s ‘fast pattern completer’ brains have been shown today to be less ra￾tional than previously supposed by economists. The new “neuroeconomics”, in

fact, has demonstrated that many choices are often made more from an emotional

than a rational approach.

Preface VII

a group of areas that have proven impervious to existing mappings in￾cludes most of the social sciences; these areas are simply too hard for tra￾ditional science.

The difficulty of finding a precise map has not stopped social scientists

from developing precise formal models and attempting to fit those precise

models to the data, and much of the methodological debate in the social

sciences concerns what implications we can draw from the vague impre￾cise mappings that one can get with existing analytic theories and data se￾ries. Critics of economics have called it almost useless - the celestial me￾chanics of a nonexistent universe. Until recently, the complaints of critics

have been ignored, not because standard economists did not recognize the

problems, but because the way we were doing economics was the best we

could do. But science, like all fields, is subject to technological change,

and recently there have been significant changes in analytic and computa￾tional technology that are allowing new theories to develop. Similar ad￾vances are occurring in empirical measurement, providing scientists with

much more data, and hence many more areas to place finer patterns on,

and in the analytics of empirical measurement, which allows the patterns

developed by theories to be brought to the data better3

. Such technological

change has been occurring in the economics profession over the last dec￾ade, and that technological change is modifying the way economics is

done. This book captures some of that change.

The new work is sometimes described as complexity theory, and in

many ways that is a helpful and descriptive term that we have both used

(Colander 2000a, b; Salzano and Kirman 2004). But it is also a term that is

often misused by the popular press and conveys to people that the com￾plexity approach is a whole new way of doing economics, and that it is a

replacement for existing economics. It is neither of those things. The com￾plexity approach is simply the integration of some new analytic and com￾putational techniques into economists’ bag of tools. We see the new work

as providing some alternative pattern generators, which can supplement

existing approaches by providing an alternative way of finding patterns

than can be obtained by the traditional scientific approach.

The problem with the use of the complexity moniker comes about be￾cause, as discussed above, individuals, by nature, are fast pattern complet￾ers. This has led some scientific reporters, and some scientists in their non-

——————

3

As usual the reality is more complicated than can be presented in a brief intro￾duction. The problem is that measurement does not stand alone, but is based on

theory. Discontent about traditional theories can lead to a search for new ways of

measurement, and improvements in the quality of data.

VIII Preface

scientific hats, to speculate about possible patterns that can follow from the

new models and techniques. As this speculation develops, the terms get

away from the scientists, and are no longer seen as simply descriptions of

certain properties of specific mathematical models, but instead as grand

new visions of how science is to be done, and of our understanding of real￾ity. Such a grandiose vision makes it seem that complexity is an alternative

to standard science, when it is actually simply a continuation of science as

usual4

.

The popular press has picked up on a number of ideas associated with

these models - ‘emergent structure’, ‘edge of order’, ‘chaos’, ‘hierarchy,

‘self organized criticality’, ‘butterfly effect’, ‘path dependency’, ‘histere￾sis’, etc. - and, using its fast-pattern completer skills, has conveyed many

of these ideas to the general population with a sense that they offer a whole

new way of understanding reality, and a replacement for standard science.

Scientists have shied away from such characterizations and have em￾phasized that while each of these terms has meaning, that meaning is in the

explicit content in the mathematical model from which they derive, not in

some general idea that is everywhere appropriate. The terms reflect a pat￾tern that economic scientists are beginning to develop into a theory that

may prove useful in understanding the economy and in developing poli￾cies. But the work is still in the beginning stages, and it is far too early to

declare it a science and a whole new way of looking at something. Scien￾tists are slow, precise, pattern completers and they recognize that the new

work has a long way be go before it will describe a meaningful pattern,

and an even longer way to go before it can be determined whether those

patterns are useful5

.

Thus, even if the complexity approach to economics is successful, it

will be a complement to, not a substitute for, existing approaches in eco￾nomics. That said, there are some hopeful signs and research in “complex￾ity” is some of the most exciting research going on in economics. The

most hopeful work is occurring in analysis of the financial sector, where

——————

4

This is not dissimilar from what has already happened for the “biological evolu￾tion” work, which was a more general, but not fundamentally different, approach

from the mechanical physical biological model.

5

In agent-based modeling (ABM), the model consists of a set of agents that en￾capsulate the behaviors of the various individuals that make up the system, and

execution consists of emulating these behaviors. In equation-based modeling

(EBM), the model is a set of equations, and execution consists of evaluating them.

Thus, “simulation” is the general term that applies to both methods, which are dis￾tinguished as (agent-based) emulation and (equation-based) evaluation. See Pa￾runak & A. (1998).

Preface IX

enormous amounts of quality data are available. But even where high qual￾ity data is not available, such as in questions of industrial organization, the

approach is changing the way the questions are conceptualized, with mar￾kets being conceptualized as dynamic rather than static as in the more tra￾ditional approach.

How the Complexity Approach Relates to the Standard

Approach

The standard theoretical approach used in economics is one loosely based

on a vision of rational agents optimizing, and is a consideration of how a

system composed of such optimizing agents would operate. The complex￾ity approach retains that same vision, and thus is simply an extension of

the current analysis. Where complexity differs is in the assumptions it al￾lows to close the model. The complexity approach stresses more local,

rather than global, optimization by agents than is done in the traditional

approach. Agent heterogeneity and interaction are key elements of the

complexity approach.

The standard approach, which developed over the last 100 years, was

limited in the methods available to it by the existing evolving analytic and

empirical technology. That meant that it had to focus on the solvable as￾pects of the model, and to structure assumptions of the model to fit the

analytics, not the problem. The analysis evolved from simple static con￾strained optimization to nonstochastic control theory to dynamic stochastic

control theory, but the general structure of the analysis - the analytic pat￾tern generating mechanism - remained the same, only more jazzed up.

In the search to focus on the solvable aspects of the model, the stan￾dard approach had to strongly simplify the assumptions of the model using

the representative agent simplification, and the consequent gaussianeity in

the heterogeneity of agents. Somehow, models the economy without any

consideration of agent heterogeneity were relied upon to find the patterns

that could exist. The complexity approach does not accept that, and pro￾poses a different vision, which is a generalization of the traditional analy￾sis. In fact, it considers the representative agent hypothesis that character￾izes much of modern macro as a possible, but highly unlikely, case and

thus does not find it a useful reference point. But these changes in assump￾tions are not without cost. The cost of making agent heterogeneity central

is that the complexity model is not analytically solvable. To gain insight

into it, researchers must make use of simulations, and generally, with

simulations, results are neither univocally nor probabilistically determined.

X Preface

The standard approach offered enormous insights, and proved highly

useful in generating patterns for understanding and applying policy. It led

to understanding of rationing situations, shadow pricing, and underlay a

whole variety of applied policy developments: cost benefit analysis, mod￾ern management techniques, linear programming, non-linear program￾ming, operations research, options pricing models, index funds … the list

could be extended enormously. It suggested that problems would develop

if prices were constrained in certain ways, and outlined what those prob￾lems would be; it led to an understanding of second order effects￾externalities, and how those second order effects could be dealt with. It

also led to actual policies - such as marketable permits as a way of reduc￾ing pollution - and underlies an entire approach to the law. Moreover, the

standard approach is far from moribund; there are many more areas where

the patterns generated by the standard approach will lead to insights and

new policies over the coming decades. Standard economics remains

strong.

Despite its academic successes there are other areas in which standard

economics has not been so helpful in generating useful patterns for under￾standing. These include, paradoxically, areas where it would seem that the

standard theory directly applies - areas such as stock market pricing, for￾eign exchange pricing, and understanding the macro economy more gener￾ally. In matching the predictions of standard theory to observed phenom￾ena, there seem to be too many movements uncorrelated with underlying

fundamentals, and some patterns, such as the arch and garch movement in

stock price data, that don’t fit the standard model. The problem is twofold -

the first is the simplicity of the model assumptions do not allow the com￾plexity of the common sense interactions that one would expect; the sec￾ond is the failure of the models to fit the data in an acceptable way.

It is those two problems that are the starting points for the complexity

approach. The reason why the complexity approach is taking hold now in

economics is because the computing technology has advanced. This ad￾vance allows consideration of analytical systems that could not previously

be considered by economists. Consideration of these systems suggested

that the results of the ‘control-based’ models might not extend easily to

more complicated systems, and that we now have a method - piggybacking

computer assisted analysis onto analytic methods - to start generating pat￾terns that might provide a supplement to the standard approach. It is that

approach that we consider the complexity approach.

It is generally felt that these unexplained observations have something

to do with interdependent decisions of agents that the standard model as￾sumes away. Moreover, when the dynamics are non-linear, local variations

from the averages can lead to significant deviations in the overall system

Preface XI

behavior. Individuals interact not only within the market; they also interact

with other individuals outside the market. Nowadays, theorists are trying

to incorporate dynamic interdependencies into the models. The problem is

that doing so is enormously complex and difficult, and there are an almost

infinite number of possibilities. It is that complexity that the papers in this

volume deal with.

In terms of policy the papers in this volume suggest that when econo￾mists take complexity seriously, they become less certain in their policy

conclusions, and that they expand their bag of tools by supplementing their

standard model with some additional models including (1) agent-based

models, in which one does not use analytics to develop the pattern, but in￾stead one uses computational power to deal with specification of models

that are far beyond analytic solution; and (2) non-linear dynamic stochastic

models many of which are beyond analytic solution, but whose nature can

be discovered by a combination of analytics and computer simulations. It

is elements of these models that are the source of the popular terms that

develop.

Developments in this new approach will occur on two dimensions. The

first is in further development of these modeling techniques, understanding

when systems exhibit certain tendencies. It is one thing to say that butterfly

effects are possible. It is quite another to say here are the precise character￾istics that predict that we are near a shift point. Until we arrive at such an

understanding, the models will be little help in applied policy. Similarly

with agent-based models. It is one thing to find an agent-based model that

has certain elements. It is quite another to say that it, rather than one of the

almost infinite number of agent based models that we could have chosen,

is the appropriate model to use as our theory.

The second development is in fitting the patterns developed to the data.

Is there a subset of aspects of reality that better fit these models than the

standard models? Are there characteristics of reality that tell us what as￾pects they are? Both these developments involve enormous amounts of

slogging through the analytics and data.

The papers in this volume are elements of that slogging through. They

are divided into four sections: general issues, modeling issues, applica￾tions, and policy issues. Each struggles with complicated ideas related to

our general theme, and a number of them try out new techniques. In doing

so, they are part of science as usual. The choice of papers highlights the

necessity to consider a multifaceted methodology and not a single method￾ology in isolation. Our goal is to give the reader a sense of the different

approaches that researchers are following, so as to provide a sense of the

different lines of work in the complexity approach.

XII Preface

It is commonly said that science progresses one funeral at a time; the

papers in this volume suggest that there is another method of progression -

one technique at a time, and as various of these techniques prove fruitful,

eventually the sum of them will lead economics to be something different

than it currently is, but it is a change that can only be seen looking back

from the future.

Part I: General Issues

The first two papers deal with broad definitional and ontological issues,

the cornerstone of economic thinking. One of the ways economists have

arrived at patterns from theory is to carefully delineate their conception of

agents, restricting the analyst to what Herbert Simon called sub rationality,

and which Vercelli, in the first paper, “Rationality, Learning, and Com￾plexity: from the Homo Economicus to the Homo Sapiens”, calls ‘very re￾strictive notions of expectations formation and learning that deny any role

for cognitive psychology’. He argues that the approach of standard eco￾nomics succeeds in simplifying the complexity of the economic system

only at the cost of restricting its theoretical and empirical scope. He states,

‘If we want to face the problems raised by the irreducible complexity of

the real world we are compelled to introduce an adequate level of epis￾temic complexity in our concepts and models’, (p 15) concluding, ‘epis￾temic complexity is not a virtue, but a necessity’.

In the second paper, “The Confused State of Complexity Economics:

An Ontological Explanation”, Perona addresses three issues: the coexis￾tence of multiple conceptions and definitions of complexity, the contradic￾tions manifest in the writings of economists who alternate between treating

complexity as a feature of the economy or as a feature of economic mod￾els, and finally the unclear status of complexity economics as an ortho￾dox/heterodox response to the failures in traditional theory. He argues that

economists supporting the complexity ideas tend to move alternatively be￾tween different conceptions of complexity, which makes it hard to follow

what their argument is. Using Tony Lawson’s ontic/theoretietic distinction,

he argues that the plurality of complexity definitions makes sense when we

observe that most of the definitions are theoretic notions, but that the ap￾parent agreement between heterodox and orthodox traditions over com￾plexity ideas is fictitious since the ‘two sides represent in fact quite differ￾ent and even opposite responses to the problems perceived in traditional

theory’. (p 14).

Preface XIII

Part II: Modeling Issues I - Modeling Economic

Complexity

The next set of papers enters into the issues of modeling. The first of these,

“The Complex Problem of Modeling Economic Complexity” by Day, de￾velops the pattern sense of science that we emphasized in the introduction,

and provides a general framework for thinking about the problem of mod￾eling complexity. Day argues that rapid progress only began in science

when repetitive patterns, which could be expressed in relatively simple

mathematical formulas, were discovered, and that the patterns developed

could provide simplification in our understanding of reality. However, this

approach left out many aspects that could not be described by simple equa￾tions.

Day argues that Walrasian general equilibrium is a theory of mind over

matter, that has shown “how, in principle a system of prices could coordi￾nation the implied flow of goods and services among the arbitrarily many

heterogeneous individual decision-makers”. The problem with the theory

is that it is about perfect coordination, while the interesting questions are to

be found in less than perfect coordination - how the process of coordina￾tion works out of equilibrium. He then goes through some of the key litera￾ture that approached the problem along these lines. He concludes with an

admonition to complexity researchers not be become intrigued with the

mathematics and models, but to concentrate on the task of explaining such

things as how governments and central banks interact with private house￾holds and business sectors, with the hope of identifying “policies that im￾prove the stability and distributional properties of the system as a whole”.

Day’s paper is the perfect introduction to the modeling sections of the

book because it provides the organizing belief of the contributors to this

volume that the work in complexity on chaotic dynamics and statistical

mechanics “provides potential templates for models of variables in any

domain whose behavior is governed by nonlinear, interacting causal forces

and characterized by nonperiodic, highly irregular, essentially unpredict￾able behavior beyond a few periods into the future”.

Above we argued that the complexity revolution was not be a revolu￾tion in the sense of an abandonment of previous work, but will be a set of

developments that occur one technique at a time, which when looked back

upon from a long enough perspective, will look like a revolution. The sec￾ond paper in this section, “Visual Recurrence Analysis: Application to

Economic Time Series” by Faggini, suggests one of those new techniques.

In the paper Faggini argues that the existing linear and non-linear tech￾niques of time series analysis are inadequate when considering chaotic

phenomena. As a supplement to standard time series techniques he argues

XIV Preface

that Recurrence Plots can be a useful starting point for analyzing non￾stationary sequences. In the paper he compares recurrence plots with clas￾sical approaches for analyzing chaotic data and detecting bifurcation. Such

detection is necessary for deciding whether the standard pattern or one of

the new complexity patterns is the pattern appropriate for policy analysis.

The third paper in this part, “Complexity of Out-of-equilibrium Play in

a Tax Evasion Game” by Lipatov, uses the same evolutionary framework

that characterizes work in complexity, but combines it with more tradi￾tional economic models, specifically evolutionary game theory with learn￾ing, to model interactions among taxpayers in a tax evasion game. The pa￾per expands on previous models of tax evasion, but adds an explicitly

characterization of taxpayer interaction, which is achieved by using an

evolutionary approach allowing for learning of individuals from each

other. He argues that the dynamic approach to tax compliance games re￾opens many policy issues, and that as a building block for more general

models, the evolutionary approach he provides can be used to consider

policy issues.

Part III: Modeling Issues II - Using Models from Physics to

Understand Economic Phenomena

Part III is also about modeling, but is focus is on adapting models from

physics to explain economic phenomena. The papers in this section ex￾plore various issues of modeling, demonstrating various mathematical

techniques that are available to develop patterns that can then be related to

observation to see if they provide a useful guide. The first paper in this

section, “A New Stochastic Framework for Macroeconomics: Some Illus￾trative Examples” by Aoki, extends the Day’s argument, starting with the

proposition that that the standard approach to microfoundations of macro￾economics is misguided, and that therefore we need a new stochastic ap￾proach to study macroeconomics. He discusses the stochastic equilibria

and ultra metrics approaches that might be used to get at the problems, and

how those approaches can provide insight into real world problems. He

gives an example of how these approaches can explain Okun’s Law and

Beveridge curves, and can demonstrate how they shift in response to mac￾roeconomic demand policies. He also shows how these new tools can re￾veal some unexpected consequences of certain macroeconomic demand

policies.

The second paper in this part, “Probability of Traffic Violations and

Risk of Crime: A Model of Economic Agent Behavior” by Mimkes, shows

the relationship between models in physics and economic models. Specifi-

Preface XV

cally he relates the system of traffic agents under constraint of traffic laws

to correspond to atomic systems under constraint of energy laws, and to

economic models of criminal behavior. He finds that the statistical La￾grange LeChatalier principle agrees with the results, and concludes by

suggesting that “similar behavior of agents may be expected in all corre￾sponding economic and social systems (situations) such as stock markets,

financial markets or social communities” (p. 11).

Muchnik and Solomon’s paper, “Markov Nets and the Nat Lab Plat￾form: Application to Continuous Double Auction”, considers Markov

Nets, which preserve the exclusive dependence of an effect even on the

event directly causing it but makes no assumption on the time lapse sepa￾rating them. These authors present a simulation platform (NatLab) that

uses the Markov Net formalisms to make simulations that preserve the

causal timing of events and consider it in the context of a continuous dou￾ble auction market. Specifically, they collect preferred trading strategies

from various subjects and simulate their interactions, determining the suc￾cess of each trading strategy within the simulation.

Arecchi, Meucci, Allaria, and Boccaletti’s paper “Synchronization in

Coupled and Free Chaotic Systems”, examines the features of a system af￾fected by heteroclinic chaos when subjected to small perturbations. They

explore the mathematics of what happens when there is an intersection

point between a stable and unstable manifold, which can create homoclinic

tangles, causing systemic erratic behavior and sensitivity to initial condi￾tions. The possibilities of such behavior should serve as a cautionary tale

to policy makers who make policy relying on the existence of systemic

stability.

Part IV: Agent Based Models

Part IV considers agent based models, which differ from the models in the

previous section in that they begin with specification of agent strategies

and do not have any analytic solution, even in principle. Instead one allows

agents with various strategies to interact in computer simulations and from

those interactions one gains knowledge about the aggregate system. This

allows the exploration of models in which the agents are assumed to have

far less information and information processing capabilities than is gener￾ally required for analytic models.

The first paper in this section, “Explaining Social and Economic Phe￾nomena by Models with Low or Zero Cognition Agents” by Omerod,

Trabatti, Glass, and Colbaugh, examines two socio-economic phenomena,

the distribution of the cumulative size of economic recessions in the US