Lecture Notes in Economics and Mathematical Systems 602 FoundingEditors: M.Beckmann H.P.Künzi ManagingEditors: Prof.Dr.G.Fandel FachbereichWirtschaftswissenschaften FernuniversitätHagen Feithstr.140/AVZII,58084Hagen,Germany Prof.Dr.W.Trockel InstitutfürMathematischeWirtschaftsforschung(IMW) UniversitätBielefeld Universitätsstr.25,33615Bielefeld,Germany EditorialBoard: A.Basile,A.Drexl,H.Dawid,K.Inderfurth,W.Kürsten Norman Ehrentreich Agent-Based Modeling The Santa Fe Institute Artificial Stock Market Model Revisited 123 Dr.NormanEhrentreich RiverSourceInvestments,LLC 262AmeripriseFinancialCenter Minneapolis,MN55474 USA [email protected] ISBN 978-3-540-73878-7 e-ISBN 978-3-540-73879-4 DOI 10.1007/978-3-540-73878-7 LectureNotesinEconomicsandMathematicalSystemsISSN 0075-8442 LibraryofCongressControlNumber:2007937522 (cid:2)c 2008Springer-VerlagBerlinHeidelberg Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerial is concerned, specificallythe rights of translation, reprinting, reuseof illustrations, recitation, broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplication ofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyright LawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtained fromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoes notimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Production:LE-TEXJelonek,Schmidt&VöcklerGbR,Leipzig Cover-design:WMXDesignGmbH,Heidelberg Printedonacid-freepaper 987654321 springer.com Meinen Eltern gewidmet. Foreword When the original Santa Fe Institute (SFI) artificial stock market was createdintheearly1990’s,thecreatorsrealizedthatitcontainedmany interesting new technologies that had never been tested in economic modeling. The authors kept to a very specific finance message in their papers, but the hope was that others would pick up where these papers left off and put these important issues to the test. Tackling the com- plexities involved in implementation has held many people back from this, and many parts of the SFI market remain unexplored. Ehren- treich’s book is an important and careful study of some of the issues involved in the workings of the SFI stock market. As Ehrentreich’s book points out in its historical perspective, the SFI market was intended as a computational test bed for a market with boundedly rational learning agents replacing the standard setup ofperfectlyrationalequilibriummodelingcommonineconomicsandfi- nance. These agents exhibit reasonable, purposeful behavior, but they are not able to completely process every aspect of the world around them. This can be viewed much more as a function of the complex- ity of the world, rather than the computational limitations of agents. In a financial world out of equilibrium, optimal behavior would re- quire knowledge of strategies being used by all the other agents, an information and computational task which seems well out of reach of any trader. The SFI market’s main conclusion was that markets where agents were learning might not converge to traditional simple rational expectations equilibria. They go to some other steady state in which a rich set of trading strategies survives in the trader population. In this steady state the market demonstrates empirical signatures that are present in most financial time series. VIII Foreword This book is an excellent reference to both the learning, and em- pirical literature in finance. It stresses the difficult empirical facts that are out of reach of most traditional financial models including per- sistent volatility and trading volume, and technical trading behavior. However, Ehrentreich’s main mission is to dig deeply into the SFI mar- ket structure to understand what is actually going on. Computational economic models can often be explored at three levels. There is sort of a big picture level where concepts such as rational expectations and boundedrationalityareexplored.Thereisalsotheverylowlevelwhere researchers discuss the nuts and bolts of different modeling languages. In between these sits a region where many of the computational learn- ing technologies are implemented. This is where technologies such as genetic algorithms, classifier systems, and neural networks drive much of what is going on. This is Ehrentreich’s area of exploration, and it is critically important to agent-based modelers since one needs to know the sensitivity of the higher level results to changes in the learning structures used beneath them. The SFI market uses two learning mechanisms extensively: the ge- netic algorithm, GA, and classifier system. Both of these are devel- opments of John Holland, one of the SFI market coauthors. The GA is a type of general evolutionary learning mechanism, and it is used in bothcomputerscienceandeconomics.Itspropertieshavebeenstudied, but it is still not completely understood. In computer science it is often studiedindifficultoptimizationproblems.Theseareproblemswithwell definedobjectives,andarequitedifferentfromthemoreopenendedco- evolutionary problems in economics where agents are competing with each other. The classifier system is an interesting learning structure that allows agents to dynamically find relevant states in the world around them. For example, actions might be conditioned on whether a stock is currently priced above a certain multiple of dividends. The classifier has the power to endogenously slice up a stream of empirical information into states of the world. Very few learning mechanisms are able to do this. With this generality comes a lot of model complexity, and many implementations of the classifier seem computationally un- wieldy. They also involve many implementation questions that need to be explored. In several chapters Ehrentreich explores some of the more impor- tant aspects of the SFI classifier implementations. He shows that the SFI classifier is sensitive to certain design characteristics. Under dif- ferent assumptions about evolution the classifier system behaves very differently from the original SFI model. Ehrentreich carefully modifies Foreword IX and explores his own operation on mutating trading strategies. Using this modified mutation causes a situation in which the SFI market is much more likely to converge to the rational expectations equilibrium, and the rich technical trading dynamic does not emerge. The results in the original SFI market are clearly sensitive to how mutation is imple- mented.Thebookgoesontodoacomparativestudybetweenmutation operators. A key issue is how many technical trading related rules are evolved, and whether the system is likely to generate lots of technical rulesby chance inthe evolutionaryprocess.The modifiedmutation op- erator does not generate many of these rules, so they never really get a foot in the door of trading activity. The SFI structure facilitates their formation, but it is possible this could be driven more by genetic drift than selection. The original SFI studies never really answered these questions, and it only looked at trading strategy formation in an indi- rect level by looking at aggregate numbers. This was a clear weakness. Ehrentreichdoessomecarefulcheckstoseeiftechnicalrulesareadding value at the agent level. It appears that they are, so many of the SFI indirect conclusions are sound. The dynamics of wealth was never part of the original SFI market. ItisaninterestingomissionthattheSFImarketneverreallyconsidered longtermwealthinaseriouswayinitsimplementation.Thisisstrange since many arguments about efficient markets thrive on the relative dynamicsoftraderwealth.Ehrentreichconcludesthatthisisacomplex problem, and there may be difficulties with some of the other studies that try to tag a wealth dynamic onto the SFI market. In my opinion thisisoneofthebiggestlimitationsoftheactualSFImarketstructure. This book is an important piece of work for understanding the dy- namics of models with interacting learning agents. I think researchers in the future will find it critical in helping them to understand the dynamics of evolutionary learning models. Most importantly, it sets an important standard for doing careful internal experiments on these markets and the learning mechanisms inside them. Brandeis University, Waltham, MA September 2007 Blake LeBaron Preface The road of science is filled with surprises. When embarking on a sci- entific journey, we probably have a specific destination in mind, but we never know whether the road will take us there nor what places we may encounter along the way. This trip was no exception. Before anyone starts reading this trav- elogue, I think that I should briefly mention a few places that I visited, but decided to pass over while writing this book. I originally aimed at converting the well-known Santa Fe Institute Artificial Stock Market (SFI-ASM) into a two stock version to study portfolio decisions of in- dividual investors. My early forays into this unknown territory yielded some interim results, but until now they are still waiting to be further examined. Instead, my road took a sudden and unexpected turn. One of the most important findings of the original SFI-ASM was the emergence of technical trading for faster learning speeds. Yet a thorough analysis of the agent’s learning algorithm suggested that this might have been caused by an ill-designed mutation operator. For a couple of years, many tests confirmed this supposition. For instance, even though tech- nical trading rules emerged in the original SFI-ASM, they were rarely acted upon. Most importantly, though, was that agents with an alter- native mutation operator discovered the homogeneous rational expec- tationsequilibrium,aresultthatfoundimmediateapprovalbyneoclas- sically inclined economists. I traveled a long way down this road. Since I considered the ex- istence of technical trading to be an empirical fact of financial mar- kets, I tried to unearth the necessary ingredients to reintroduce it into my model. Nothing that I devised, neither social learning nor explicit herding mechanisms, succeeded in that endeavor. There was, however, XII Preface another surprise waiting behind the supposedly final turn of my jour- ney. One newly designed test showed a slight superiority of technical trading rules in the original model. A side-trip all the way down to population genetics finally proved that my agents were committing a mistake by deciding to ignore technical trading rules. Again, parts of my prior research were discarded, and a new chapter was written ex- plaining why I and previous researchers went wrong in interpreting the simulation results. I hope that this chapter will prove most useful for anyresearchinvolvinggeneticalgorithms.Mypriorbeliefthattechnical tradingwasanartificiallyintroducedmodelartifacthadalsocausedme to visit some previous studies about wealth levels. I was able to show that the SFI-ASM was not designed to address any questions related to wealth. Fortunately, this part was unaffected by the breakdown of the initial motivation to look into the wealth generation process. A long journey with such detours was certainly not easy. I could not have arrived at the final destination without the tremendous support andencouragementthatIhavefoundalongtheway.Aboveall,Iwishto thank my parents Werner and Ellinor Ehrentreich, for without them, I would not have had the opportunity to embark on this journey. I would also like to thank Reinhart Schmidt for letting me choose my destination and for giving me the freedom to follow my own path. Among the numerous friends, colleagues, and conference participants who have contributed in many ways are Manfred Ja¨ger, Ulrike Neyer, RalfPeters,MartinKlein,Heinz-PeterGaller,JosephFelsenstein,Alan Kirman, and James Stodder. Of course, this book would not have been finished without the contributions by Blake LeBaron. Not only did he play a major role in the creation of the model that I set out to extend, then critiqued, and finally confirmed, he also often helped and clarified many questions that I was pondering. Many thanks also go to Lars Schiefner, Doris Storch, and Klaus Renger, especially for their help during the final stages of this project. Last, but not least, I thank Tanya Novak for her patience and help, especially for her proofreading. Nonetheless, I absolve her from all remaining mistakes and typos and credit them to my cats, Zina and Francesco, who stubbornly insisted on their input by jumping on the keyboard. I now hope that the reader will find it useful to visit the places that I have found worthwhile to mention in this book. Minneapolis, MN September 2007 Norman Ehrentreich Contents Part I Agent-Based Modeling in Economics 1 Introduction ......................................... 3 2 The Rationale for Agent-Based Modeling ............ 5 2.1 Introduction....................................... 5 2.2 The Representative Agent Modeling Approach ......... 7 2.2.1 Avoiding the Lucas-Critique ................... 8 2.2.2 Building Walrasian General Equilibrium Models .. 9 2.2.3 Representative Agents and the Fallacy of Composition ................................. 10 2.2.4 Expectation Formation in Markets with Heterogeneous Investors ....................... 11 2.3 Rational Expectations and Disequilibrium Dynamics.... 13 2.4 The Economy as an Evolving Complex Adaptive System 14 2.5 Some Methodological Aspects of Agent-Based Simulations 16 3 The Concept of Minimal Rationality ................. 19 3.1 Introduction....................................... 19 3.2 Economic, Bounded, and Situational Rationality ....... 21 3.3 Situational Analysis, Minimal Rationality, and the Prime Directive .................................... 24 3.4 Minimal Rationality and the Phillips-Curve ........... 26 4 Learning in Economics ............................... 29 4.1 Introduction....................................... 29 4.2 Definitions of Learning.............................. 29 4.3 Rationality-Based Learning Models................... 31 4.4 Biologically Inspired Learning Models................. 32