Introductory Materials

Agent-Based Computational Economics (ACE)
and Related Topics

Last Updated: 26 February 2024

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Table of Contents: Key Issues On-Line Guides for Newcomers Other Basic Introductory Readings Additional Introductory Materials Agents and Morality Math Formalisms for Agent-Based Modeling Big Data & Agent-Based Modeling Historical Antecedents Classic Critiques Miscellaneous On-Line Materials

Site and Software Release Disclaimer:

Unfortunately, links to many excellent introductory ACE/ABM/CAS resources originally posted at this site are now broken and had to be removed. Below are annotated links to still-available resources that visitors might find useful and/or of historical interest.

Key Issues

• What is a complex system? A complex adaptive system?
• Does the understanding of an observed system (sand pile, washing machine, cockroach, city, economy,...) require knowing how to construct it? And what might "constructing it" mean?
• Does the understanding of an observed system require knowing how it came about historically?
• Agent-based Computational Economics (ACE) is roughly defined as the computational study of economic processes as open-ended dynamic systems of interacting agents. What is an "agent"? And why all the emphasis on learning, interactions, and endogenous network formation among interacting "agents"?
• One goal of ACE researchers is to understand the possible genesis of persistently observed economic regularities (e.g., the use of money) by using "culture-dish" computational experiments to grow economies that reliably display these regularities when started from certain specified initial conditions. Is this a meaningful goal? A feasible goal?
• Another goal of ACE researchers is to experimentally test alternative institutional designs for economic processes (e.g., the sensitivity of market efficiency to alternative bidding protocols). Is this a meaningful goal? A feasible goal?
• Can ACE facilitate the scientific study of economic processes?

On-Line Guides for Newcomers

• Robert Axelrod and Leigh Tesfatsion, An On-Line Guide for Newcomers to Agent-Based Modeling in the Social Sciences (html,44KB)

  Abstract: This site provides web support materials (readings and demonstration software) for Robert Axelrod and Leigh Tesfatsion, "A Guide for Newcomers to Agent-Based Modeling in the Social Sciences" (pdf,46KB), in Leigh Tesfatsion and Kenneth L. Judd (Eds.), Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics (Table of Contents,html), Handbooks in Economics Series, Elsevier/North-Holland, Amsterdam, 2006.

• Jason M. Barr et al., The Future of Agent-Based Research in Economics: A Panel Discussion (pdf,138KB), Eastern Economic Journal 34 (2008), 550-565.

  Abstract: Exceptionally thoughtful commentaries on the theory and practice of ABM by a group of co-moderators (Jason Barr, Troy Tassier, Leanne Ussher) and panelists (Blake LeBaron, Shu-Heng Chen, Shyam Sunder) at the Eastern Economic Association Meeting held in Boston, March 7, 2008. Well worth reading.

• Federico Bianchi and Flaminio Squazzoni, "Agent-Based Models in Sociology" (pdf,1MB), WIREs Computational Statistics, Vol. 7, July/August (2015), 284–306. doi:10.1002/wics.1356

  Abstract: This article reviews sociological applications of agent-based modeling over the past twenty years, with a stress on explanatory achievements and methodological insights. Topics covered include: cooperation and social norms; reciprocity; reputation; social punishment; trust; conventions; social influence; cultural and opinion dynamics; collective behavior; and social inequality.

• Eric Bonabeau, "Agent-Based Modeling: Methods and Techniques for Simulating Human Systems" (pdf,265KB), Proceedings of the National Academy of Sciences, Supplement 3, May 14, 2002, 7280-7287.

  Abstract: After a brief introduction to the basic principles of agent-based simulation, four real-world application areas are discussed: flow simulation, organizational simulation, market simulation, and diffusion simulation. Business applications within these areas are then described and analyzed.

• Paul L. Borrill and Leigh Tesfatsion, "Agent-Based Modeling: The Right Mathematics for the Social Sciences?" (pdf,3.5MB), pp. 228-258 in J.B. Davis and D.W. Hands (eds.), Elgar Companion to Recent Economic Methodology, Edward Elgar Publishers, February 2011, 560pp. ISBN-13: 9781848447547

  Abstract: This study provides a basic introduction to agent-based modeling (ABM), with a primary focus on its applicability for social science research.

• Shu-Heng Chen, "Varieties of Agents in Agent-Based Computational Economics: A Historical and an Interdisciplinary Perspective" (Preprint pdf,1.2MB), Journal of Economic Dynamics and Control 36(1), January 2012, 1-25 (doi).

  Abstract: This thoughtful and comprehensive study traces the origins of agent-based computational economics (ACE) through four different gateways: namely, study of market processes; study of cellular automata with fixed rules of behavior; evolution-of-cooperation tournaments with programmed strategies; and experiments with autonomous human-like agents (artificial life).

• Duncan K. Foley, Chapter 1: "Introduction (pp. 23-72) (pdf,369K), in Peter S. Albin and Duncan K. Foley (Eds.), Barriers and Bounds to Rationality: Essays on Economic Complexity and Dynamics in Interactive Systems, Princeton Studies in Complexity, Princeton University Press, NJ, 1998.

  Abstract: This wide-ranging introductory chapter by a seminal contributor to economic complexity theory covers: Economic complexity puzzles; economic models of fully rational behavior; definitions and measures of complexity; complexity in cellular automata; modeling of complex social and economic interactions; complexity, rationality, and social interaction; and towards a robust theory of action and society.

• Nigel Gilbert, The Idea of Agent-Based Modeling (pdf, 365KB), Chapter 1 in Agent-Based Modeling, Sage, 2008, 98pp.

  Abstract: This introductory book chapter begins with a brief overview of agent-based modeling (ABM). It then contrasts ABM with other more more familiar forms of modeling and describes several examples of current agent-based modeling research.

• Andrew G. Haldane, The Dappled World (pdf,2.3MB), GLS Shackle Biennial Memorial Lecture, Bank of England, 10 November 2016.

  Abstract: Although (the recent) crisis in economics is a threat for some, for others it is an opportunity -- an opportunity to make a great leap forward, as Keynes did in the 1930s. For the students in this room, there is the chance to rethink economics with as clean a sheet of paper as you are ever likely to find. That is perhaps why the numbers of students applying to study economics has shot up over recent years. This is one of the silver linings of the crisis. No discipline could ask for a better endowment. But seizing this opportunity requires a re-examination of the contours of economics and an exploration of some new pathways. That is what I wish to do in this lecture..."

• Dirk Helbing, The Automation of Society is Next: How to Survive the Digital Revolution (pdf, 5.3MB), Version 1.0, 2015, 266pp.

  Abstract: Artificial intelligence is rapidly evolving far beyond its originally envisioned role as a tool providing assistance to humans. Experts predict that artificially intelligent devices will be able to perform many tasks better than humans by 2025; even highly skilled jobs will be at risk. Helbing asks how society can manage this digital revolution in a manner that enhances the quality of human life, including the preservation of human dignity, privacy, and individual freedoms. To support his points, the author draws on theoretical analyses, data analytics, human-subject lab experiments, and computational experiments with agent-based computer models for which agents have cognitive capabilities.

• Alan Kirman, "The Economic Entomologist: An Interview with Alan Kirman" (pdf,236KB), Erasmus Journal for Philosophy and Economics 4(2), Autumn, 2011.

  Abstract: This article presents an engaging wide-ranging interview with Alan Kirman, one of the seminal explorers and advocates of an interactionist approach to the study of economic systems to bridge the divide between individual behavior and aggregate patterns.

• Charles M. Macal and Michael J. North, "Tutorial on Agent-Based Modelling and Simulation" (pdf,359KB), Journal of Simulation, Vol. 4, 2010, 151–162.

  Abstract: This article provides a brief introduction to agent-based modeling and simulation. The authors illustrate the main concepts and foundations, discuss some recent applications across a variety of disciplines, and identify methods and toolkits for developing agent models.

• Matteo Richiardi, "Agent-Based Computational Economics: A Short Introduction" (pdf,227KB), The Knowledge Engineering Review 27(2), 2012, 137-149.

  Abstract: "In this paper we provide a brief overview of the main characteristics of agent-based computational economics. We discuss its points of strength, with respect to analytical models, and its weaknesses. The latter are mainly related to how the results of a simulation model can be interpreted, and how the structural parameters of the model can be estimated. We then show how these problems can be dealt with."

• John D. Sterman, "All Models are Wrong: Reflections on Becoming a Systems Scientist" (pdf,4.2MB), System Dynamics Review 18 (2002), 501-531.

  Abstract: "...Becoming an effective systems thinker requires the rigorous and disciplined use of scientific inquiry skills so that we can uncover our hidden assumptions and biases. It requires respect and empathy for others and other viewpoints. Most important, and most difficult to learn, systems thinking requires understanding that all models are wrong and humility about the limitations of our knowledge. Such humility is essential in creating an environment in which we can learn about the complex systems in which we are embedded and work effectively to create the world we truly desire."

• Leigh Tesfatsion, "Agent-Based Computational Economics: Overview and Brief History" (Preprint,pdf,170KB), (KeynoteSSC,pdf,1.5MB), Chapter 4 (pp. 41-58) in: Ragupathy Venkatachalam (Ed.), Artificial Intelligence, Learning and Computation in Economics and Finance, Springer Cham, February 2023, 325pp.

  Abstract: Scientists and engineers seek to understand how real-world systems work and could work better. Any modeling method devised for such purposes must simplify reality. Ideally, however, the modeling method should be flexible as well as logically rigorous; it should permit model simplifications to be appropriately tailored for the specific purpose at hand. Flexibility and logical rigor have been the two key goals motivating the development of Agent-based Computational Economics (ACE), a completely agent-based modeling method characterized by seven specific modeling principles. This perspective provides an overview of ACE, a brief history of its development, and its role within a broader spectrum of experiment-based modeling methods.

• Leigh Tesfatsion, "Modeling Economic Systems as Locally-Constructive Sequential Games" [ (WP,pdf,679KB), (Talk Slides,1MB)], Journal of Economic Methodology, Vol. 24, Issue 4, 2017, 384-409.

  Abstract: Real-world economies are open-ended dynamic systems consisting of heterogeneous interacting participants. Human participants are decision-makers who strategically take into account the past actions and potential future actions of other participants. All participants are forced to be locally constructive, meaning their actions at any given time must be based on their local states; and participant actions at any given time affect future local states. Taken together, these essential properties imply real-world economies are locally-constructive sequential games. This paper discusses a modeling approach, Agent-based Computational Economics (ACE), that permits researchers to study economic systems from this point of view. ACE modeling principles and objectives are first concisely presented and explained. The remainder of the paper then highlights challenging issues and edgier explorations that ACE researchers are currently pursuing.

• Leigh Tesfatsion, "Elements of Dynamic Economic Modeling: Presentation and Analysis" (WP,pdf,630KB), Eastern Economic Journal 43(2), 2016, 192-216. doi:10.1057/eej.2016.2

  Abstract: The primary goal of these introductory notes is to promote the clear presentation and rigorous analysis of dynamic economic models, whether expressed in equation or agent-based form. A secondary goal is to promote the use of initial-value state space modeling with its regard for historical process, for cause leading to effect without the external imposition of global coordination constraints on agent actions. Economists who claim to respect individual rationality should not be doing for their modeled economic agents what in reality these agents must do for themselves.

• Leigh Tesfatsion, Tutorial on Agent-Based Computational Economics (ACE) (Talk Slides,2.4MB), Latest Revision: 2 December 2016.

  Abstract: After a brief overview of the ACE modeling approach, multiple types of ACE applications are reviewed.

• Leigh Tesfatsion, Agent-Based Modeling: A Bridge Between Games & Social Sciences (pdf,997KB).

  Abstract: This short presentation, designed for younger newcomers to Agent-Based Modeling (ABM), starts by giving a brief introduction to ABM using examples from the movies. It next invites readers to participate in a "hands on" demonstration of ABM by playing a version of the Schelling Tipping Game using a checkerboard and tokens. (The Schelling Tipping Game was first introduced in 1978 by Tom Schelling in Micromotives and MacroBehavior.) It then introduces readers to the Schelling Tipping Game Demonstration Software developed by Chris Cook (see below) as well as the SimSeg test bed, an elaboration of the Schelling Tipping Game suitable for serious social science research. It concludes by pointing readers to a website where numerous commercial applications of ABM are discussed.

  Schelling Tipping Game Demonstration Software (html)

• Paola Tubaro, Agent-Based Computational Economics: A Methodological Appraisal (pdf,176KB), EconomiX Working Paper 2009-42, University of Paris, July 2009.

  Abstract: "This paper is an overview of `Agent-based Computational Economics' (ACE), an emerging approach to the study of decentralized market economies, in methodological perspective. It summarizes similarities and differences with respect to conventional economic models, outlines the unique methodological characteristics of this approach, and discusses its implications for economic methodology as a whole."

• Arthur Turrell, Agent-Based Models: Understanding the Economy from the Bottom Up (pdf,850KB), Quarterly Bulletin, Q4, Bank of England, Dec. 16, 2016, 173-188.

  Abstract: The author (Advanced Analytics Division, Bank of England) provides a clear, concise, non-technical overview of agent-based modeling, with a particular stress on its applicability for economics.

• Tamás Vicsek, "Complexity: The Bigger Picture" (pdf,71KB), Nature, Vol. 418, Issue 6894, 11 July 2002, p. 131.

  Abstract: In this short essay, Vicsek describes how computer simulation fits into the scientific enterprise. The goal is to "capture the principal laws behind the exciting variety of new phenomena that become apparent when the many units of a complex system interact."

Other Basic Introductory Readings

• W. Brian Arthur, "Complexity Economics: A Different Framework for Economic Thought" (pdf,781KB), Santa Fe Institute Working Paper: 2013-4-2012.

  Abstract: "This paper provides a logical framework for complexity economics. Complexity economics builds from the proposition that the economy is not necessarily in equilibrium: economic agents (firms, consumers, investors) constantly change their actions and strategies in response to the outcome they mutually create. This further changes the outcome, which requires them to adjust afresh. Agents thus live in a world where their beliefs and strategies are constantly being "tested" for survival within an outcome or "ecology" these beliefs and strategies together create. Economics has largely avoided this nonequilibrium view in the past, but if we allow it, we see patterns or phenomena not visible to equilibrium analysis. These emerge probabilistically, last for some time and dissipate, and they correspond to complex structures in other fields. We also see the economy not as something given and existing but forming from a constantly developing set of technological innovations, institutions, and arrangements that draw forth further innovations, institutions and arrangements."

• W. Brian Arthur, Complexity Economics, Oxford University Press, 2013.

  Abstract: This book surveys the birth and growth over the past twenty-five years of a different approach to economics, termed complexity economics. This approach holds that an economy is not necessarily in equilibrium, that computation as well as mathematics is useful in economics, that increasing as well as diminishing returns may be present in an economic situation, and that the economy is not something given and existing but forms from a constantly developing set of institutions, arrangements, and technological innovations. Questions addressed include: What does this different way of thinking about the economy offer? How exactly does it work and where does it fit in? Will it replace neoclassical economics, or be subsumed into neoclassical economics? And under what logic, if any, does it operate?

• Rob Axtell, "Agent-Based Computing in Economics" (pdf,256KB), presented at the VII Trento Summer School, July 2006.

• David F. Batten, "Preface" plus Chapter 1:"Chance and Necessity" (pdf preprint-no figures,247KB) plus Chapter 8: "Artificial Economics" (pdf preprint-no figures,173KB) in Discovering Artificial Economics: How Agents Learn and Economies Evolve, Perseus Books, Westview Press, 2000.

  IMPORTANT NOTE: The Batten book is unfortunately out of print. However, a pdf file for the entire Batten book (including figures) can be accessed here (pdf,17MB).

• Mark Buchanan, Forecast: What Physics, Meteorology, and the Natural Sciences can Teach Us About Economics, Bloomsbury, New York, 2013.

  Abstract: "In all these books (on the global economic crisis), I felt one thing was missing - an examination of the peculiar concepts of economic thinking, of the atmosphere of ideas of modern economic theory, which swayed many people to believe that the tumultuous history of economics and finance, a history of almost continual crises and disruption going back four hundred years, had somehow come to a miraculous end in our era because of the markets' self-regulating nature and tendency towards `equilibrium.' I've written this book to help fill this gap, and also to explore more constructive ideas for building a more realistic and more natural understanding of economic systems."

• Shu-Heng Chen, Agent-Based Computational Economics, Book Series: Advances in Experimental and Computable Economics, Routledge Publishers, October 2013, 256pp.

  Abstract: "This book provides a review of the development of agent-based computational economics (ACE) from a perspective on how artificial economic agents are designed under the influences of complex sciences, experimental economics, artificial intelligence, evolutionary biology, psychology, anthropology and neuroscience. The review also includes how these agents are networked by using ideas from physics, mathematics and sociology. Despite this rich interdisciplinary colour, the book has a simple fundamental pursuit, that is, to use ACE to clothe economics with Marshall’s spirit: `Economics, like biology, deals with a matter, of which the inner nature and constitution, as well as outer form, are constantly changing.'"

• Claudio Cioffi-Revilla, Introduction to Computational Social Science: Principles and Applications, Springer, 2014, 358pp.

  Abstract: "This reader-friendly textbook is the first work of its kind to provide a unified introduction to computational social science (CSS). Four distinct methodological approaches are examined in detail: namely, automated social information extraction, social network analysis, social complexity theory, and social simulation modeling."

• Joshua M. Epstein and Robert Axtell, Growing Artificial Societies: Social Science from the Bottom Up, MIT Press/Brookings, MA, 1996 (Review, JEL, March 1998, 233-234, pdf, 35KB).

  Abstract: Using a relatively simple agent-based computational framework called Sugarscape in which traders exchange sugar (or sugar and spice), the authors show how the complex adaptive systems paradigm can be applied to the study of social phenomena. Illustrative applications include trade, migration, group formation, combat, interaction with an environment, transmission of culture, propagation of disease, and population dynamics.

• Mark Granovetter, "A Theoretical Agenda for Economic Sociology" (pdf,253KB), in M. F. Guillen, R. Collins, P. England, and M. Meyer (eds.), Economic Sociology at the Millenium, Russell Sage Foundation, New York, 2001.

  Abstract: Economic sociology is concerned with the study of economic processes imbedded in social contexts and relational (interaction) networks. This paper reassesses what theoretical agenda a structural economic sociology might pursue, and where this agenda fits with the main concerns of sociology and economics.

• Cars Hommes, "Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems", Cambridge University Press, January 2013. Introductory materials (including Chapter 1) can be viewed (here,6MB).

  Abstract: "Recognising that the economy is a complex system with boundedly rational interacting agents, the book presents a theory of behavioral rationality and heterogeneous expectations in complex economic systems and confronts the nonlinear dynamic models with empirical stylized facts and laboratory experiments. ... The complexity tools - bifurcations, chaos, multiple equilibria - discussed in this book will help students, researchers and policy makers to build more realistic behavioral models with heterogeneous expectations to describe financial market movements and macro-economic fluctuations, in order to better manage crises in a complex global economy."

• Robert E. Marks and Nicolaas J. Vriend, "Agent-Based Computational Economics Overview" (pdf,71KB), The Knowledge Engineering Review 27(2), 2012, 115-122.

  Abstract "The Knowledge Engineering Review is an outstanding journal in Computer Science. The guest editors and contributors to these two Special Issues are economists. Why is this so? In recent years there has been a growing dialogue between economists and computer scientists, to our mutual benefit. The Special Issues are devoted to nine papers (five in Part 1 and four in Part 2) in which economists survey aspects of the field of agent-based computational economics (ACE) models, and in some cases report on new findings in several areas of application. As such, we hope they have something to offer both computer scientists and economists."

• Robert E. Marks and Nicolaas J. Vriend (guest eds.), Special Issue on Agent-Based Computational Economics, The Knowledge Engineering Review 27(2), 2012.

• Steven F. Railsback and Volker Grimm, Agent-Based and Individual-Based Modeling: A Practical Introduction, Princeton University Press, 2012, 321 pp, ISBN 978-0-691-13673-8. ( Book Website: Supplemental Materials)

  Abstract: This textbook is designed for university courses and self-instruction by physical, biological, and social scientists. Its four parts provide: an introduction to the basics of modeling and individual- or agent-based modeling; in-depth experience with an established conceptual framework for designing models and with programming models in NetLogo software; familiarity with the "pattern-oriented modeling" strategy for developing theory for agent behavior and calibrating models; and experience analyzing models to produce both applied and theoretical science.

• Leigh Tesfatsion, Agent-Based Computational Economics: A Constructive Approach to Economic Theory (pdf,253KB), in Leigh Tesfatsion and Kenneth L. Judd (eds.), Handbook of Computational Economics, Volume 2: Agent-Based Computational Economics, Handbooks in Economics Series, Elsevier/North-Holland, the Netherlands, 2006.

  Abstract: This chapter explores the potential advantages and disadvantages of ACE for the study of economic systems. General points are concretely illustrated using an ACE model of a two-sector decentralized market economy. Six issues are highlighted: Constructive understanding of production, pricing, and trade processes; the essential primacy of survival; strategic rivalry and market power; behavioral uncertainty and learning; the role of conventions and organizations; and the complex interactions among structural attributes, behavior, and institutional arrangements.

• Leigh Tesfatsion, Economic Agents and Markets as Emergent Phenomena (pdf,167KB), Proceedings of the National Academy of Sciences U.S.A., Vol. 99, Suppl. 3, 2002, 7191-7192.

  Abstract: A brief overview of recent work in agent-based computational economics is provided, with a stress on the application areas highlighted in the NAS Sackler Colloquium session "Economic Agents and Markets as Emergent Phenomena" held in October 2001.

• Leigh Tesfatsion, Agent-Based Computational Economics: Growing Economies from the Bottom Up (pdf,216KB), Volume 8, Number 1, 2002, 55-82, published by the MIT Press. Also available is a modified version (pdf,269KB) ("Agent-Based Computational Economics," Economics Working Paper No. 1, Iowa State University, Ames, IA, June 2002, Revised August 2003) directed more specifically to economists.

  Abstract: This study is an extended version of the previous PNAS overview. The main objectives and defining characteristics of agent-based computational economics (ACE) are outlined, and similarities and distinctions between ACE and artificial life research are clarified. Eight ACE research areas are identified, and a number of publications in each area are highlighted for concrete illustration. Open questions and directions for future ACE research are also considered. The study concludes with a discussion of the potential benefits of the ACE approach, as well as some potential difficulties.

• Leigh Tesfatsion, Introduction to the special ACE double-issue for the Journal of Economic Dynamics and Control (Volume 25, Numbers 3-4, March 2001, pp. 281-293), Introduction to the special ACE issue for Computational Economics (Volume 18, Number 1, October 2001), and Guest Editorial for the special issue of the IEEE Transactions on Evolutionary Computation on Agent-Based Modelling of Evolutionary Economic Systems (Volume 5, Number 5, October 2001, pp. 437-441).

• Leigh Tesfatsion and Kenneth L. Judd (eds.), Handbook of Computational Economics, Volume 2: Agent-Based Computational Economics, Handbooks in Economics Series, Elsevier/North-Holland, the Netherlands, 2006, 904pp. Preface, Table of Contents, and Abstracts.

  Abstract: This handbook volume surveys recent research on Agent-based Computational Economics (ACE), the computational study of economic processes modeled as dynamic systems of interacting agents. Empirical referents for "agents" in ACE models can range from individuals or social groups with learning capabilities to physical world features with no cognitive function. The handbook includes 16 chapters surveying ACE research, 6 general perspectives on ACE (by Arthur, Axelrod, Epstein, Howitt, Leijonhufvud, and Schelling), and an appendix providing a guide for newcomers to agent-based modeling in the social sciences (by Axelrod and Tesfatsion). Topics covered include: learning; empirical validation; network economics; social dynamics; financial markets; innovation and technological change; organizations; market design; automated markets and trading agents; political economy; social-ecological systems; computational laboratory development; and methodological issues.

• Paola Tubaro, "Computational economics", pp. 209-227 in J. B. Davis and D. W. Hands (eds.), The Elgar Companion to Recent Economic Methodology, Aldershot: Edward Elgar, 2011.

  Abstract: This chapter provides a thoughtful wide-ranging discussion of the origins, chararacteristic features, and future prospects of the agent-based computational economics (ACE) methodology.

Additional Introductory Materials

• ACE/CAS Introductory Books

• Agent-Based Modeling Colloquium: Capturing Complexity Through Agent-Based Modelling, published in the Proceedings of the National Academy of Sciences, Vol. 99, Suppl. 3, 2002.

• Agent-Based Modelling, an ABM resource site maintained by Brett Parris (Monash University, Australia).

• W. Brian Arthur, Steven N. Durlauf, and David A. Lane, The Economy as an Evolving Complex System II, Proceedings Volume XXVII, Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, Reading, MA, 1997.

• Sunny Y. Auyang, Synthetic Analysis of Complex Systems I - Theories (html,11pp), circa 2000.

  Abstract: This thoughtful essay by independent researcher Sunny Auyang addresses the question "what is complexity." The author attempts to extract the commonly shared ideas implicit in many formalized conceptions of complexity and also in the general way that people tend to think about complicated situations. One important distinction not stressed by the author, however, is that living agents in social and biological systems (as opposed to inanimate elements in purely physical systems) can exert some degree of deliberate forward-looking control over the formation and evolution of their interaction networks.

• Sunny Y. Auyang, "Foundations of Complex-System Theories in Economics, Evolutionary Biology, and Statistical Physics", Cambridge University Press, Cambridge, UK, 1998.

  Abstract: "This book continues my effort to uncover the categorical framework of objective thought as it is embedded in scientific theories and common sense....Composition is not merely congregation; the constitutents of a compound interact and the interaction generates complicated structures. ...How does science represent and explain the complexity of composition?"

• Robert Axelrod, Advancing the Art of Simulation in the Social Sciences (pdf,119KB), Japanese Journal for Management Information System, Special Issue on Agent-Based Modeling, Vol. 12, No. 3, Dec. 2003.

  Abstract: The author offers advice for doing social science simulation research, focusing on the programming of a simulation model, analyzing the results, and sharing the results with others. The essay is scheduled to appear in a special issue on agent-based modeling in the Japanese Journal for Management Information Systems.

• Rob Axtell, Why Agents? On the Varied Motivations for Agent Computing in the Social Sciences (pdf,115KB), Center on Social and Economic Dynamics, Working Paper No. 17, November 2000.

• Rob Axtell, The New Coevolution of Information Science and Social Science (pdf,198KB), Working Paper, Brookings Institution, 2003.

  Abstract: This paper briefly reviews the ways in which exponentially increasing information technology (IT) capabilities are reshaping the social sciences, and how results from the social sciences are in turn making their way into computer and information sciences. The author argues that one specific IT-facilitated development in particular -- multi-agent systems -- "holds out the promise of fundamentally altering the ways in which social science models are conceived, built, explored, and evaluated."

• Andrei Borshchev and Alexei Filippov, "From System Dynamics and Discrete Event to Practical Agent-Based Modeling: Reasons, Techniques, and Tools" (pdf,308KB), Proceedings, 22nd International Conference of the System Dynamics Society, Oxford, England, July 25-29, 2004.

  Abstract: The authors compare three major paradigms in simulation modeling: system dynamics, discrete event modeling, and agent-based modeling.

• Shu-Heng Chen, Lakhmi Jain, and Chung-Ching Tai, Computational Economics: A Perspective from Computational Intelligence, Idea Group Inc., 318pp., 2006.

  Abstract: "(This book) provides models of various economic and financial issues while using computational intelligence as a foundation. The scope of this volume comprises finance, economics, management, organizational theory and public policies. It explains the ongoing and novel research in this field, and displays the power of these computational methods in coping with difficult problems with methods from traditional perspectives."

• David Colander (ed.), The Complexity Vision and the Teaching of Economics, Edward Elgar Pub., June 2000, 328 pp., ISBN: 1-840-64252-1.

  Abstract: From the publisher: "This ground-breaking book focuses on the implications of the complexity vision, such as that held by economists at the Santa Fe Institute, for the teaching of economics. ... It asks the question: how would the teaching of economics change if complexity is taken seriously? An outstanding group of contributors, including Brian Arthur, Buz Brock, and Duncan Foley, provide interesting and provocative answers to that question in a non-technical and highly accessible style."

• Bruce Edmonds, Pablo Lucas, Juliette Rouchier, and Richard Taylor, "Human Societies: Understanding Observed Social Phenomena" (pdf,442KB), pp. 709-748 in Bruce Edmonds and Ruth Meyer (Eds.), Simulating Social Complexity, Springer, 2013.

  Abstract: This chapter discusses and illustrates fifteen different possible simulation goals, both abstract and concrete.

• Joshua Epstein, Agent-Based Computational Models and Generative Social Science, Complexity, Vol. 4/No. 5, May/June 1999, 41-60.

• Joshua M. Epstein, Generative Social Science: Studies in Agent-Based Computational Modeling, Princeton University Press, Princeton, 356pp., 2006.

  Abstract: "Agent-based computational modeling is changing the face of social science. In (this book), Joshua Epstein argues that this powerful, novel technique permits the social sciences to meet a fundamentally new standard of explanation, in which one `grows' the phenomenon of interest in an artificial society of interacting agents: heterogeneous, boundedly rational actors, represented as mathematical or software objects."

• Nigel Gilbert, Agent-Based Social Simulation: Dealing with Complexity (pdf,281KB), centre for Research on Social Simulation, University of Surrey, Guildford, UK, 18 December 2004.

  Abstract: This non-technical but carefully written paper examines recent advances in the application of computer simulation to the social sciences. Illustrative examples are used to show how this new methodology is appropriate for analyzing social phenomena that are inherently complex, and how it encourages experimentation and the study of emergence.

• Nigel Gilbert, Agent-Based Models, Quantitative Applications in the Social Sciences, Volume 153, SAGE Publications, Inc., 2008.

  Abstract: The author reviews a range of illustrative agent-based modeling (ABM) applications. He also provides practical advice regarding the designing and building of ABMs, model verification and empirical validation, planning a modeling project, and the writing of scholarly ABM articles. Last but not least, he provides a glossary of terms, an annotated list of resources, advice on programming languages and toolkits, and a step-by-step worked out example of an ABM implementation.

• John H. Holland, Hidden Order: How Adaptation Builds Complexity, Addison-Wesley, 1995, ISBN 0-201-40793-0.

  Abstract: Clear and thoughtful discussion of the characteristics of complex adaptive systems, both man-made and natural. Proposes a possible tractable approach to the modelling of complex adaptive systems. Illustrates in concrete terms how this approach might be applied to the modelling of ecological systems (the Echo framework).

• Nicholas R. Jennings, On Agent-Based Software Engineering (pdf,257KB), Artificial Intelligence 117 (2000), 277-296, copyright © 2002 Elsevier Science B.V. All rights reserved.

  Abstract: Agent-based computing represents an exciting new synthesis both for Artificial Intelligence (AI) and, more generally, Computer Science. It has the potential to significantly improve the theory and the practice of modeling, designing, and implementing computer systems... The standpoint of this analysis is the role of agent-based software in solving complex, real-world problems. In particular, it will be argued that the development of robust and scalable software systems requires autonomous agents that can complete their objectives while situated in a dynamic and uncertain environment, that can engage in rich, high-level social interactions, and that can operate within flexible organizational structures.

• Steven Johnson, Emergence: The Connected Lives of Ants, Brains, Cities, and Software, Scribner, 288 pp., Sept. 2001. ISBN: 0-684-86875-X.

  Abstract: From the publisher: "Drawing upon evolutionary theory, urban studies, neuroscience, and computer games, Emergence is a guidebook to one of the key components of twenty-first-century culture. Until recently, Johnson explains, the disparate philosophers of emergence have worked to interpret the world. But today they are starting to change it. This book is the riveting story of that change and what it means for the future. If you've searched for information on the Web, played a recent video game, or accepted a collect call using voice recognition software, you've already encountered the new world of artificial emergence. Provocative, engaging, and sophisticated, Emergence puts you on the front lines of a sweeping revolution in science and thought."

• David A. Kendrick, P. Ruben Mercado, and Hans M. Amman, Computational Economics, Princeton University Press, Princeton, NJ, 2006.

  Abstract: Chapters 11 through 14 of this book provide illustrative GAMS/Matlab implementations of genetic algorithms as used in evolutionary games and portfolio models and agent-based computational macroeconomic and environmental models.

• Steven Levy, Artificial Life: A Report from the Frontier Where Computers Meet Biology, Random House, NY, 1992.

  Abstract: Dated, now, but still a highly entertaining introduction to the field of artificial life.

• Francesco Luna and Alessandro Perrone (eds.), Agent-Based Methods in Economics and Finance: Simulations in Swarm, Kluwer Academic Publishers, Dordrecht and London, 2001.

• Michael W. Macy and Robert Willer, "From Factors to Actors: Computational Sociology and Agent-Based Modeling" (pdf,134KB), Annual Review of Sociology, Vol. 28, 2002, pp. 143-166. Published article available at JSTOR.

  Abstract: While written for sociologists, this review article should be of value to all agent-based modelers. It places agent-based modeling in its historical context, explains its meaning and goals, provides many good examples, and offers useful advice to those who want to try it for themselves.

• John H. Miller and Scott E. Page, Complex Adaptive Systems: Introduction to Computational Models of Social Life, Princeton Studies in Complexity, Princeton University Press, 284pp., March 2007.

  Abstract: "This book provides the first clear, comprehensive, and accessible account of complex adaptive social systems, by two of the field's leading authorities. Such systems -- whether political parties, stock markets, or ant colonies -- present some of the most intriguing theoretical and practical challenges confronting the social sciences. Engagingly written, and balancing technical detail with intuitive explanations, (this book) focuses on the key tools and ideas that have emerged in the field since the mid-1990s, as well as the techniques needed to investigate such systems."

• John Miller and Scott E. Page, "The Standing Ovation Problem" (pdf,141KB), Complexity, Vol. 9, No. 5, May/June 2004, pp. 8-16.

  Abstract: Miller and Page use audience ovation to introduce many key ABM themes, in particular the emergence of collective behavior, and to provide specific modeling suggestions suitable for implementation by newcomers to the field. As a public performance draws to a close, and audience members begin to applaud and some even tentatively to stand, will a standing ovation ensue or not? This is the famous Standing Ovation Problem (SOP) inspired by the seminal work of Thomas Schelling on the relationship between micro decisions and macro behaviors (see the Section on Complexity and ABM, above). Miller and Page use the SOP to illustrate how complex social dynamics can arise from the interactions among simple personal choices, in this case to stand or not. They argue (p. 9) that the success of the SOP as an expository device is that it forces modelers "to confront the core methodological issue in complex adaptive social systems, namely, how does one model a system of thoughtful, interacting agents in time and space?"

• Philip Mirowski, Machine Dreams: Economics Becomes a Cyborg Science, Cambridge University Press, Cambridge, UK, 655 pp., 2002. ISBN: 0-521-77526-4.

  Abstract: From a review by Duncan Foley (New School University): "(This book) is an astonishing performance of synthetic scholarship. Mirowski traces the present-day predicaments of economic theory to its intellectual reformulation and institutional restructuring by military funding and in the crucibles of World War II and the cold war. His demonstration that the mathematical economics of the postwar era is a complex response to the challenges of `cyborg science,' the attempt to unify the study of human beings and intelligent machines through John von Neumann's general theory of automata, is bound to be controversial. His critics, however, will have to contend with a breathtakingly wide range of published and unpublished evidence in fields ranging from psychology to operations research he presents. This noir history of economic thought will change its readers' understanding of twentieth-century economics profoundly."

• Denis Phan and Frédéric Amblard, Agent-Based Modelling and Simulation in the Social and Human Sciences, The Bardwell Press, Oxford, UK, 2007.

  Abstract: "This volume brings together contributions from leading researchers in the field of agent-based modeling and simulation. ... The research case studies and theoretical approaches discussed in this book are designed to introduce beginners and experts alike to the current state of play in this new and exciting field of social science."

• Jonathan Rauch, Seeing Around Corners (pdf,4.2MB), The Atlantic, April 2002.

  Abstract: This feature article traces the history of artificial societies from its roots in the work of Thomas Schelling to Axtell and Epstein's Sugarscape Model. Rauch discusses (Brookings Institution) research on Zipf distributions, A-societies and the Anasazi tribe, to posit that the construction of artificial communities provides social scientists with a method to predict the outcomes of particular policy interventions.

• Mitchel Resnick, Unblocking the Traffic Jams in Corporate Thinking: Models of Decentralized Systems, Complexity, Vol. 3/No. 4, March/April 1998, pp. 27-30.

• Mitchel Resnick, Turtles, Termites, and Traffic Jams: Explorations in Massively Parallel Microworlds, MIT Press, Cambridge, MA, 1994, ISBN: 0-262-18162-2.

  Abstract: Focuses on decentralized systems and self-organizing phenomena. Examines how and why people resist decentralized ideas, and describes a new computer language, StarLogo, designed to help people explore decentralized systems and move beyond the centralized mindset.

• Thomas Schelling, Micromotives and Macro Behavior, Norton, N.Y., 1978.

  Abstract: From the publisher: "Through familiar and readily grasped examples, Professor Schelling demonstrates what happens when behavior in the aggregate is more than a simple summation of individual behaviors, how members of a society tend to be blind to the collective consequences of their separate decisions, and why attempts to infer individual intentions from group phenomena are tricky at best and often downright impossible."

• Karl Sigmund, Games of Life: Explorations in Ecology, Evolution, and Behavior, Oxford University Press, 1993.

  Abstract: Great introductory presentation of various models of evolution. Topics include: population ecology and chaos; random drift and chain reactions; population genetics; evolution and sex; evolutionary game theory; and reciprocity and the evolution of cooperation.

• Herbert Simon, "The Architecture of Complexity" (pdf,549KB), pp. 193-230 in The Sciences of the Artificial, Second Edition, The MIT Press, Cambridge, MA, 1982.

  Abstract: Simon informally defines a "complex system" to be a system made up of a large number of parts that interact in a non-simple way. He considers a number of complex systems encountered in the behavioral sciences, from families to formal organizations, and describes features that are common in a wide variety of such systems. His central theme (p. 196) is that "complexity frequently takes the form of hierarchy and that hierarchic systems have some common properties independent of their specific content." He discusses the design advantages of nearly decomposable subsystems with a hierarchical organization of their parts. He also conjectures that complex systems evolve from simple systems much more rapidly if there are stable intermediate forms along the way, hence evolution favors hierarchic over non-hierarchic systems.

• Flaminio Squazzoni, "The Impact of Agent-Based Models in the Social Sciences After 15 Years of Incursions (pdf,248KB), History of Economic Ideas, XVIII/2010/2.

  Abstract: The author provides a retrospective overview of the impact of agent-based modeling (ABM) on social science over the past fifteen years. He discusses contributions that ABM has made to economics, sociology, anthropology, and the behavioral sciences, new fields that ABM has opened up, and issues that ABM social science researchers need to address in the future.

• Flaminio Squazzoni, Agent-Based Computational Sociology, John Wiley, 256pp, May 2012.

  Abstract: The idea of this book is that most of the intriguing social phenomena of our time, such as international terrorism, social inequality, and urban ethnic segregation, are consequences of complex forms of agent interaction that are difficult to observe methodically and experimentally. This book looks at a new research stream that makes use of advanced computer simulation modelling techniques to spotlight agent interaction that allows us to explain the emergence of social patterns. It presents a method to pursue analytical sociology investigations that look at relevant social mechanisms in various empirical situations, such as markets, urban cities, and organisations.

Agents and Morality

• The site OpenAI is devoted to the discovery and enactment of paths to safe artificial general intelligence.

• Luciano Floridi and J. D. Sanders, "On the Morality of Artificial Agents" (pdf,302KB), Minds and Machines, Vol. 14, Issue 3 (August), 2004, 349-379.

  Abstract: Artificial agents (AAs), particularly but not only those in Cyberspace, extend the class of entities that can be involved in moral situations. For they can be conceived of as moral patients (as entities that can be acted upon for good or evil) and also as moral agents (as entities that can perform actions, again for good or evil). In this paper, we clarify the concept of agent and go on to separate the concerns of morality and responsibility of agents (most interestingly for us, of AAs). We conclude that there is substantial and important scope, particularly in Computer Ethics, for the concept of moral agent not necessarily exhibiting free will, mental states or responsibility. This complements the more traditional approach, common at least since Montaigne and Descartes, which considers whether or not (artificial) agents have mental states, feelings, emotions and so on.

• Alice Pavaloiu and Utku Kose, "Ethical Artificial Intelligence - An Open Question" (pdf,665KB), Journal of Multidisciplinary Developments, Vol. 2, Issue 2, 2017, 15-27.

  Abstract: Artificial Intelligence (AI) is an effective science which employs strong enough approaches, methods, and techniques to solve unsolvable real-world based problems. Because of its unstoppable rise towards the future, there are also some discussions about its ethics and safety. Shaping an AI-friendly environment for people and a people-friendly environment for AI can be a possible answer for finding a shared context of values for both humans and robots. In this context, objective of this paper is to address the ethical issues of AI and explore the moral dilemmas that arise from ethical algorithms, from pre-set or acquired values. In addition, the paper will also focus on the subject of AI safety. As general, the paper will briefly analyze the concerns and potential solutions to solving the ethical issues presented and increase readers’ awareness on AI safety as another related research interest.

Mathematical Formalisms for Agent-Based Modeling

• The Foundation for Intelligent Physical Agents (FIPA) is an IEEE Computer Society standards organization that promotes agent-based technology and the interoperability of its standards with other technologies.

• Amelia Badica, Bogdan Trawiński, and Ngoc Thanh Nguyen (Eds.), Recent Developments in Computational Collective Intelligence (pdf,4.2MB), Studies in Computational Intelligence, Volume 513, Springer, 2014.

  Abstract: Computational Collective Intelligence (CCI) is a sub-field of Artificial Intelligence that focuses on soft computing methods enabling group decisions or processing of knowledge among autonomous units acting in distributed environments. This edited volume consists of 19 extended revised works originally presented at the 5th International Conference on CCI, held on September 11-13, 2013, in Coraiova, Romania.

• Paul L. Borrill and Leigh Tesfatsion, "Agent-Based Modeling: The Right Mathematics for the Social Sciences?" (pdf,3.5MB), pp. 228-258 in J.B. Davis and D.W. Hands (eds.), Elgar Companion to Recent Economic Methodology, Edward Elgar Publishers, February 2011, 560pp. ISBN-13: 9781848447547

  Abstract: This paper maintains that agent-based modeling (ABM) is a powerful blend of classical and constructive mathematics that is particularly well suited for social science research.

• Shu-Heng Chen, "Computational Intelligence in Agent-Based Computational Economics", Chapter 13 (pp. 517-594) in J. Fulcher and L.C. Jain (Eds.), Computational Intelligence: A Compendium, SpringerLink Book Series, Studies in Computational Intelligence, Volume 115, Springer-Berlin/Heidelberg, 2008.

  Abstract: This chapter reviews the algorithmic foundations of agent-based computational economics. It also introduces the field known as "computational intelligence" and discusses its use in agent-based computational economics and its relevance for economics and finance in general.

• Russell Cooper, "Dynamic Programming: An Overview" (pdf,286KB), February 14, 2001.

• Joshua M. Epstein, "Remarks on the Foundations of Agent-Based Generative Social Science" (pdf,187KB), Chapter 34 (pp. 1585-1604) in L. Tesfatsion and K. L. Judd (Eds.), Handbook of Computational Economics Volume 2: Agent-Based Compuational Economics, Handbooks in Economics 13, North-Holland, 2006.

  Abstract: This chapter treats a variety of epistemological issues surrounding generative explanation in the social sciences, and discusses the role of agent-based computational models in generative social science.

• Joshua M. Epstein, "Agent_Zero: Toward Neurocognitive Foundations for Generative Social Science," Princeton University Press, Hardcover, Feb. 23, 2014 (Illustrated Edition), 272pp.

  Abstract (From the Publisher): "In this pioneering synthesis, Joshua Epstein introduces a new theoretical entity: Agent_Zero. This software individual, or "agent," is endowed with distinct emotional/affective, cognitive/deliberative, and social modules. Grounded in contemporary neuroscience, these internal components interact to generate observed, often far-from-rational, individual behavior. When multiple agents of this new type move and interact spatially, they collectively generate an astonishing range of dynamics spanning the fields of social conflict, psychology, public health, law, network science, and economics."

• Paul Erickson, The World the Game Theorists Made (Book Review), Chicago: University of Chicago Press, ISGN 978-022609717-6, 2015, 217pp.

  Abstract: As detailed in the comprehensive review of this book by Hunter Heyck in OEconomia, the author Paul Erickson describes game theory as a `great sequence of debates... about the prospects for building a mathematical theory of rational decision-making." The book begins with a discussion of von Neumann and Morgenstern's 1944 book Theory of Games and Economic Behavior, continues on through a discussion of the "Nashification" of game theory into a search for noncooperative Nash equilibria in the late 1980s, and ends by discussing the "fragmentation" of game theory in the 1990s into a set of tools for describing behaviors in relation to incentive structures.

• Magda Fontana, "Computer Simulations, Mathematics, and Economics" (pdf,269KB), Working Paper No. 06/2005, University of Torino, 2005. (Note: This paper was published with minor revisions as “Computer Simulations, Mathematics, and Economics”, Rivista Internazionale di Scienze Economiche e Commerciali, vo. 53(1), 2006, pp. 96-124.)

  Abstract: "This paper suggests a systematisation of the relationship between simulations, mathematics, and economics. In particular, it traces the evolution of simulation techniques, comments on some of the contributions that deal with their nature, and, finally, illustrates with some examples their influence on economic theory."

• Volker Grimm, Uta Berger, Finn Bastiansen, Sigrunn Eliassen, Vincent Ginot, Jarl Giske, John Goss-Custard, Tamara Grand, Simone K. Heinz, Geir Huse, Andreas Huth, Jane U. Jepsen, Christian Jørgensen, Wolf M. Mooij, Birgit Müller, Guy Pe'er, Cyril Piou, Steven F. Railsback, Andrew M. Robbins, Martha M. Robbins, Eva Rossmanith, Nadja Rüger, Espen Strand, Sami Souissi, Richard A. Stillman, Rune Vabø, Ute Visser, and Donald L. DeAngelis, "A Standard Protocol for Describing Individual-Based and Agent-Based Models" (pdf,249KB), Ecological Modelling 198(1-2), 2006, 115-126.

  Abstract: This paper introduces the Overview, Design concepts, and Details (ODD) protocol for agent-based modeling.

• Volker Grimm, Uta Berger, Donald L. DeAngelis, J. Gary Polhill, Jarl Giske, and Steven F. Railsback, "The ODD Protocoll: A Review and First Update" (pdf,249KB), Ecological Modelling 221, 2010, 2760-2768.

  Abstract: "The `ODD' (Overview, Design concepts, and Details) protocol was published in 2006 to standardize the published descriptions of individual-based and agent-based models (ABMs). The primary objectives of ODD are to make model descriptions more understandable and complete, thereby making ABMs less subject to criticism for being irreproducible. We have systematically evaluated existing uses of the ODD protocol and identified, as expected, parts of ODD needing improvement and clarification. Accordingly, we revise the definition of ODD to clarify aspects of the original version and thereby facilitate future standardization of ABM descriptions. We discuss frequently raised critiques in ODD but also two emerging, and unanticipated, benefits: ODD improves the rigorous formulation of models and helps make the theoretical foundations of large models more visible. Although the protocol was designed for ABMs, it can help with documenting any large, complex model, alleviating some general objections against such models."

• Volker Grimm and Steven F. Railsback, "Designing, Formulating, and Communicating Agent-Based Models" (pdf,392KB), in A. J. Heppenstall, A. T. Crooks AT, L. M. See, and M. Batty (Eds.), Agent-based Models of Geographical Systems, Springer, Dordrecht, 2012, 361-378.

  Abstract: This paper discusses two approaches for the design, formulation, and communication of agent-based models: The Overview, Design concepts, and Details (ODD) protocol, which provides design patterns for agent-based model (ABM) development and for the description of ABMs in publications; and Pattern-Oriented Modeling (POM), a set of strategies for using observed system patterns to ensure that an ABM captures the salient aspects of the system.

• Volker Grimm, Gary Polhill, and Julia Touza, "Documenting Social Simulation Models: The ODD Protocol as a Standard" (pdf,278KB), in B. Edwards and R. Meyer (Eds.), Simulating Social Complexity, Understanding Complex Systems, Springer-Verlag Berlin Heidelberg, 2013.

  Abstract: This chapter discusses the importance of documenting simulation models and encourages the use of the ODD protocol to facilitate this documentation. An annotated example of the use of ODD is provided for concrete illustration. For those interested in applying the ODD protocol, the authors have provided an ODD Template (Word).

• Kenneth L. Judd, "Computationally Intensive Analyses in Economics" (pdf,115KB), in Leigh Tesfatsion and Kenneth L. Judd (editors), Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics (Preface, Table of Contents, & Abstracts,html), Handbooks in Economics Series, Elsevier/North-Holland, Amsterdam, the Netherlands, 2006.

  Abstract: Computer technology presents economists with new tools, but also raises novel methodological issues. This essay discusses the challenges faced by computational researchers, and proposes some solutions.

• Reinhard Laubenbacher, Abdul S. Jarrah, Henning Mortveit, and S. S. Ravi, "A Mathematical Formalism for Agent-Based Modeling" (pdf,253KB), arXiv:0801.0249v1 [cs.MA], 31 December 2007.

  Abstract: This work contains a brief exposition of some known mathematical frameworks that can model multi-agent systems. The focus is on one such framework, namely that of finite dynamical systems. Both deterministic and stochastic versions of this framework are discussed.

• Kenneth A. Lloyd, Jr., "A Category-Theoretic Approach to Agent-Based Modeling and Simulation" [ (Paper,605KB), (Slides,442KB)], Swarmfest 2010, Santa Fe, NM.

  Abstract: Category theory is a mathematical formalism for the study of systems, including system elements, coupling, structure, behavior and morphism. The goal of this paper and slide presentation is to demonstrate the potential usefulness of category theory for the study and practice of agent-based modeling and simulation.

• Birgit Müller et al., "Standardised and Transparent Model Descriptions for Agent-Based Models: Current Status and Prospects" (pdf,519KB), Environmental Modeling & Software 55 (2014), 156-163.

  Abstract: "Agent-based models are helpful to investigate complex dynamics in coupled human-natural systems. However, model assessment, model comparison and replication are hampered to a large extent by a lack of transparency and comprehensibility in model descriptions. In this article we address the question of whether an ideal standard for describing models exists. We first suggest a classification for structuring types of model descriptions. Secondly, we differentiate purposes for which model descriptions are important. Thirdly, we review the types of model descriptions and evaluate each on their utility for the purposes."

• William B. Powell, "Perspectives of Approximate Dynamic Programming" (pdf,421KB), Annals of Operations Research, Springer, 2012. DOI 10.1007/s10479-102-1077-6

  Abstract: This article maintains that the approximate dynamic programming algorithms developed by researchers in a wide variety of disciplines for seemingly distinct types of applications in fact share common themes. The author shows that these algorithms can be divided into three main approaches based on the types of decision variables that are considered: discrete action spaces; low-dimensional continuous decisions; and high-dimensional decisions.

• Hazhir Rahmandad and John Sterman, "Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models" [ (Paper,pdf,380KB), [ (Supplement,pdf,195KB)], Management Science, Vol. 54, No. 5, May 2008, 998-1014.

  Abstract: "When is it better to use agent-based (AB) models, and when should differential equation (DE) models be used? Whereas DE models assume homogeneity and perfect mixing within compartments, AB models can capture heterogeneity across individuals and in the network of interactions among them. AB models relax aggregation assumptions, but entail computational and cognitive costs that may limit sensitivity analysis and model scope. Because resources are limited, the costs and benefits of such disaggregation should guide the choice of models for policy analysis. Using contagious disease as an example, we contrast the dynamics of a stochastic AB model with those of the analogous deterministic compartment DE model.

• David L. Sallach, "Categorical Social Science: Theory, Methodology, and Design" (pdf,241KB), WCSS Conference, Taiwan, 2012.

  Abstract: This paper argues that category theory provides an effective mathematical framework for the representation of social complexities.

• David L. Sallach, "Recognition-Based Logic and Social Conflict: Toward a Topos Model" (pdf,505KB), AESCS Meeting, Tokyo, 2013.

  Abstract: This paper argues that category theory, and more specifically topos categories, provide a mathematical formalism that can facilitate social modeling in both an expressive and rigorous form.

• Flaminio Squazzoni, Ed., Epistemological Aspects of Computer Simulation in the Social Sciences, Invited and selected papers from the Second International Workshop on Epistemological Perspectives on Simulation (EPOS 2006, Brescia, Italy), Springer-Verlag Berlin Heidelberg, 2009.

  Abstract: The papers in this volume stress epistemological and methodological issues, such as the relevance of empirical foundations for agent-based simulations, the role of theory, the concepts and meanings of emergence, and the trade-off between simplification and complexification of models.

• Shyam Gouri Suresh, "Rational Economic Models of Homo Sapiens" (pdf,344KB), Social Science Research Network (SSRN:ID4235655), March 2023.

  Abstract (Abbreviated Summary): This essay first describes how economic modeling has evolved over time and across different schools of economic thought. In particular, it delves into rational-agent and rational-expectations paradigms, and it describes how these paradigms have been challenged by behavioral economic findings and by macroeconomic events such as the great recession. The essay concludes by noting that the successful addressing of these challenges could require the modeling of agents with distinctly non-rational behavior. Merely tinkering along the edges to somehow incorporate inconvenient behavioral biases into an expanded definition of rational behavior is woefully inadequate today, especially since the exponential increase in computational power allows modelers to think in terms of simulation models that are not constrained by the traditional problem of analytical tractability.

• Leigh Tesfatsion, Elements of Dynamic Economic Modeling: Presentation and Analysis (pdf,630KB), Eastern Economic Journal 43(2), 2016, 192-216. doi:10.1057/eej.2016.2

  Abstract: The primary goal of these introductory notes is to promote the clear presentation and rigorous analysis of dynamic economic models, whether expressed in equation or agent-based form. A secondary goal is to promote the use of initial-value state space modeling with its regard for historical process, for cause leading to effect without the external imposition of global coordination constraints on agent actions. Economists who claim to respect individual rationality should not be doing for their modeled economic agents what in reality these agents must do for themselves.

• Leigh Tesfatsion, "Modeling Economic Systems as Locally-Constructive Sequential Games" [ (WP,pdf,679KB), (Talk Slides,1MB)], Journal of Economic Methodology, Vol. 24, Issue 4, 2017, 384-409.

  Abstract: Real-world economies are open-ended dynamic systems consisting of heterogeneous interacting participants. Human participants are decision-makers who strategically take into account the past actions and potential future actions of other participants. All participants are forced to be locally constructive, meaning their actions at any given time must be based on their local states; and participant actions at any given time affect future local states. Taken together, these essential properties imply real-world economies are locally-constructive sequential games. This paper discusses a modeling approach, Agent-based Computational Economics (ACE), that permits researchers to study economic systems from this point of view. ACE modeling principles and objectives are first concisely presented and explained. The remainder of the paper then highlights challenging issues and edgier explorations that ACE researchers are currently pursuing.

• Leigh Tesfatsion, Game Theory: Basic Introduction (slides)

  Abstract: Basic game theory definitions, plus illustrative presentation and analysis of various two-player games (e.g.,the prisoner's dilemma game).

• Leigh Tesfatsion, Solution Analysis Techiques for Parameterized Systems (Slides,173KB)

  Abstract: Short notes on computational techniques for analyzing the solutions of parameterized systems. Partitions of the solution space based on solution attributes of interest induce corresponding parameter space partitions with interesting regularities. (An extreme example of this is the famous Mandelbrot Set.) The solutions for parameterized nonlinear systems can also be tracked over user-specified parameter paths.

• Leigh Tesfatsion, "Cellular Automata: Basic Introduction" (1.5MB)

• Leigh Tesfatsion, "Introductory Notes on the Structural and Dynamical Analysis of Networks" (pdf,2.3MB)

• Leigh Tesfatsion, "Agent-Oriented Programming: Introduction" (pdf,117KB)

• Leigh Tesfatsion, Adaptive Computation Methods for Nonlinear Systems. Methods (with software implementations) featured at this site include: nonlocal automated sensitivity analysis (NASA), for the tracking of solutions for parameterized nonlinear systems over parameter intervals; tracking of eigenvalues and eigenvectors for parameterized matrices over parameter intervals; adaptive homotopy continuation; and the FEED algorithm for the fast efficient evaluation of higher-order partial derivatives.

• Gianluca Violante, "Notes on Discrete Time Stochastic Dynamic Programming (pdf,167KB), Spring 2000.

• John von Neumann, Theory of Self-Reproducing Automata, University of Illinois Press, 1966. (Edited and completed by Arthur W. Burks)

Big Data and Agent-Based Modeling

Paola D'Orazio, "Understanding the link between computational behavioral economics and the Big Data revolution: Towards a new paradigm in Macroeconomics?" (pdf,496KB), Duke Forest Conference 2016, Durham, NC, USA, Nov 29-30, 2016.

Abstract: The author considers the relationship among data, information, and knowledge for economic systems. The author discusses the possible emergence of a new paradigm for (macro)economics that takes agent-based computational modeling as a starting point and exploits the increasing availability of Big Data to provide detailed empirically-grounded specifications for agent behaviors.

Historical Antecedents

• The American Association of Artificial Intelligence (AAAI) provides extensive links to AI-related readings and sites.

• The International Journal of Microsimulation

• Kellyn F. Arnold, Wendy J. Harrison, Alison J. Heppenstall, Bark S. Gilthorpe, "DAG-Informed Regression Modelling, Agent-Based Modelling and Microsimulation Modelling" (pdf,423KB), International Journal of Epidemiology 48(1), Feb, 2019, 243-253.

  Abstract: "...We clarify (the) distinction (between directed acylic graph (DAG) informed regression modeling, microsimulation, and agent-based modeling) by briefly reviewing the history of each method, which provides a context for their similarities and differences, and casts light on the types of research questions that they have evolved (and thus are well suited) to answering. ... The distinct historical evolutions of (these methods) have given rise to distinct features of the methods themselves, and provide a foundation for critical comparison. Not only are the three methods well suited to addressing different types of causal questions, but, in doing so, they place differing levels of emphasis on fixed and random effects, and also tend to operate on different timescales and in different timeframes."

• Elisa Baroni and Matteo Richiardi, Orcutt's Vision: 50 Years On (pdf,380KB), Working Paper No. 65, Laboratorio R. Revelli, Collegio Carlo Alberto, October 2007.

  Abstract: "Fifty years have passed since the seminal contribution of Guy Orcutt [Orcutt, 1957], which gave birth to the field of Microsimulation. We survey, from a methodological perspective, the literature that followed, highlighting its relevance, its pros and cons vis-`a-vis other methodologies, and pointing out the main open issues."

• Robert L. Bennett and Barbara R. Bergmann, A Microsimulated Transactions Model of the United States Economy (Chapters 1-2, pdf, 1.5M), Johns Hopkins University Press, Baltimore, MD, 1986. [Note: Chapters 1-2 are reprinted with permission of the publishers.]

  Abstract: This seminal work develops an empirically-grounded state-space modeling of an economy formulated at the level of the decision-making processes of microeconomic units (firms, consumers, financial intermediaries) and government units (local, state, federal). Each decision-making unit is modeled as a collection of hypothesized if-then decision rules specified constructively (recursively) as state-conditioned transition processes, thus respecting historical cause-effect relationships. Initial conditions, decision-making processes, and modeled institutional arrangements are strongly based on empirical data.

• Barbara Bergmann, "Micro-to-Macro Simulation: A Primer with a Labor Market Example" (pdf,427KB), Journal of Economic Perspectives 4(1), Winter 1990, 99-116.

  Abstract: The author motivates her work as an introduction to microsimulation. In actual content, however, her innovative labor market application (implemented in Fortran) is closer in spirit to an agent-based model, with dynamics driven by worker-firm interactions, rather than to a standard microsimulation model with dynamics driven by pre-specified state transition probabilities.

• Magnus Boman and Einar Holm, Multi-Agent Systems, Time Geography, and Microsimulations (pdf,298KB), Chapter 4 (pp. 95-118) in Mats-Olov Olsson and Gunnar Sjöstedt (Eds.), Systems Approaches and Their Application, Springer, 2005.

  Abstract: The authors seek to unify two paradigms: (i) microsimulations, used in the social sciences; and (ii) multi-agent systems, used in computer science and increasingly in the social sciences.

• Kalman J. Cohen, "Simulation of the Firm", The American Economic Review, 50(2), 1960, 534–540.

  Abstract: This perceptive article, written in 1960, forcefully and clearly sets out the conceptual case for "agent-based computational economics" years in advance of the software tools permitting its practical realization.

• Kurt Dopfer and Jason Potts (Eds.), The New Evolutionary Economics, Edward Elgar Publishing, 2014.

  Abstract: This three-volume set includes seventy-seven selected articles in evolutionary economics covering 1976-2012. The three volumes cover micro analysis, meso analysis, and macro analysis, respectively.

• Gunner Eliasson, Swedish Micro to Macro Firm-Based Simulation Model (MOSES), initiated in 1974.

  Abstract: The model integrates a Schumpeterian type creative destruction process with the Stockholm School concepts of Ex Ante plans, Ex Post realizations that systematically differ over time, setting the model apart from the static general equilibrium model. His current research is focused on the role of micro agents, featuring entrepreneurial creation, the formation of new firms, their life and death and endogenous populations of firms in economic systems evolution. In this analysis MOSES appears as a model approximation of a more general theory of an Experimentally Organized Economy that grows through entrepreneurial competition and selection. This this theoretical economy competence bloc theory explains the commercialization of new innovative technologies and the efficiency of that selection."

• Gunner Eliasson, "Why Complex, Data Demanding and Difficult to Estimate Agent-Based Models? Lessons from a Decades Long Research Program" (pdf,607KB), International Journal of Microsimulation 11(1) 4-60.

  Abstract: "(T)he Swedish micro firm to macroeconomic systems modelling project presented in this essay (was) initiated almost 45 years ago. This model is presented as a Reference model for theoretical and empirical studies, with the ambition to understand the roles of the "birth, life and death" of business agents in the evolution of a self-coordinated market economy, without the help of a Walrasian central planner. Mathematical simulation is argued to be the effective tool for such theoretical and empirical analyses."

• Roger Frantz and Leslie Marsh (eds), Minds, Models, and Milieux: Commemorating the Centennial of the Birth of Herbert Simon, Palgrave Macmillan, UK, 2016, 310pp.

  Abstract: "This book is a collection of specially commissioned chapters from philosophers, economists, political and behavioral economists, cognitive and organizational psychologists, computer scientists, sociologists and permutations thereof as befits the polymathic subject of this book – Herbert Simon."

• Rainer Hegselmann, "Thomas C. Schelling and James M. Sakoda: The Intellectual, Technical, and Social History of a Model" (pdf,2.6KB), Journal of Artificial Societies and Social Simulation 20(3) 15, 2017 (electronic). DOI: 10.18564/jasss.3511

  Abstract: This impressive 155-page work, twenty years in the making, is a must-read for history of science buffs. The primary goal of the author is to provide proper recognition of James M. Sakoda who, in his 1949 dissertation submitted to the University of California at Berkeley, developed a checkerboard model specifically designed to permit the linking of individual micro actions to macro social phenomena. A secondary goal of the author is to clarify the relationship of Sakoda's checkerboard model, now largely forgotten, to the famous checkerboard model independently conceived by Thomas C. Schelling in the early 1970s. In pursuit of these two goals, the author provides the reader with a fascinating evidence-based account of the birth and early development of computational social science.

• Aki Lehtinen and Jaakko Kuorikoski, "Computing the Perfect Model: Why Do Economists Shun Simulation?" (pdf,115KB), Philosophy of Science 74 (July 2007) pp. 304–329.

  Abstract: "Like other mathematically intensive sciences, economics is becoming increasingly computerized. Despite the extent of the computation, however, there is very little true simulation. Simple computation is a form of theory articulation, whereas true simulation is analogous to an experimental procedure. Successful computation is faithful to an underlying mathematical model, whereas successful simulation directly mimics a process or a system. The computer is seen as a legitimate tool in economics only when traditional analytical solutions cannot be derived, i.e., only as a purely computational aid. We argue that true simulation is seldom practiced because it does not fit the conception of understanding inherent in mainstream economics. According to this conception, understanding is constituted by analytical derivation from a set of fundamental economic axioms. We articulate this conception using the concept of economists' perfect model. Since the deductive links between the assumptions and the consequences are not transparent in ‘bottom-up' generative microsimulations, microsimulations cannot correspond to the perfect model and economists do not therefore consider them viable candidates for generating theories that enhance economic understanding."

• Jinjing Li and Cathal O'Donoghue, "A Survey of Dynamic Microsimulation Models: Uses, Model Structure and Methodology" (pdf,487KB), International Journal of Microsimulation 6(2), 2013, 3-55.

  Abstract: "More than 10 years ago O’Donoghue (2001a) surveyed the dynamic microsimulation models that had been developed up to that point. However many of the barriers mentioned have been gradually overcome in the last decade. This paper surveys the development and practices in dynamic microsimulation over the past decade, and discusses the methodological challenges today. It provides an overview of the methodological choices made in more than 60 known dynamic microsimulation models and examines the advantages and disadvantages of different practices. In addition, this paper reviews the main progress made in the field and explores how future microsimulation models could evolve potentially."

• Thomas S. Ray (Department of Zoology, University of Oklahoma), Introduction to Artificial Life, Lecture Notes, 1996.

  Abstract: "Artificial Life (AL) extends the field of biology by allowing us to study living forms other than those occurring naturally on Earth. In this way, AL bears the same relationship to biology that synthetic chemistry does to chemistry. Some of the most significant advances in AL have been in the area of synthetic evolutions within computers. One of the major currents in this work has been to move towards systems which evolve freely within the digital medium, like the evolution by natural selection in the carbon medium that generated life on Earth. The primary objective of this work is to provoke digital evolution to generate complexity within the digital medium, comparable in magnitude to the complexity of organic life."

• Matteo Richiardi, "The missing link: Agent-Based Models and Dynamic Microsimulation" (pdf,615KB), Chapter 1 (pp. 3-15) in S. Leitner and F. Wall (eds.), Artificial Economics and Self Organization: Agent-Based Approaches to Economics and Social Systems. Lecture Notes in Economics and Mathematical Systems, vol. 669, Springer, Berlin, 2013.

  Abstract: "In this note I pay tribute to two early works by Barbara Bergmann and Gunnar Eliasson which, though firmly grounded in the dynamic microsimulation literature, can be considered as the first examples of large-scale agent-based models. These attempts at building complete micro-to-macro computational models of the economy are important not only in a history of economic thought perspective, but also to encourage convergence of the two approaches in developing credible alternatives to DSGE models."

• Raffaello Seri, Davide Secchi, and Mario Martinoli (2022), "Randomness, Emergence, and Causation: A Historical Perspective of Simulation in the Social Sciences" (Preprint,pdf,545KB), to appear in: S. Albeverio et al. (eds.), Complexity and Emergence, Springer Proceedings in Mathematics & Statistics 383, Springer Nature Switzerland AG.

  Abstract: "This chapter is a review of a selection of simulation models, with special reference to the social sciences. Three critical aspects are identified—i.e. randomness, emergence and causation—that may help understand the evolution and the main characteristics of these simulation models. Several examples illustrate the concepts through a historical perspective."

• John Sterman, System Dynamics Modeling: Tools for Learning in a Complex World (pdf,141KB), California Management Review 43(4), Summer 2001, 8-25.

  Abstract: This article provides an introduction to Systems Dynamics (SD), a differential-equations based modeling approach originally developed by Jay Forrester at MIT in the 1950s. SD emphasizes "system thinking," characterized by Sterman as the ability to see the world as a complex system in which everything is connected to everything else.

• Leigh Tesfatsion, CAS/AL/ABM/ACE Syllabus of Readings: 1996-2006

  Abstract: This website could be of historical interest. Originally established in 1996, it highlights pioneering work on complex adaptive systems (CAS), artificial life (AL), agent-based modeling (ABM), and agent-based computational economics (ACE) through approximately 2006. The following topics are covered: Introductory overviews; evolutionary computation; robotics; biological evolution; social evolution; economic and social network formation; classic critiques; software development; and commercial applications. By 2006, given the rapidly increasing activity in all of these areas, it became too unwieldly to maintain a site with this breadth of coverage. ACE research had been posted at the ACE Website since the launching of the ACE Website in 1996. After 2006, a variety of more specialized subsites were developed at the ACE Website in order to accommodate postings of CAS/AL/ABM-related materials of particular interest to ACE researchers.

• Harold W. Watts, Distinguished Fellow: An Appreciation of Guy Orcutt (pdf,270KB), Journal of Economic Perspectives 5(1), Winter 1991, 171-179.

Classic Critiques

• Daniel C. Dennett, Brainstorms: Philosophical Essays on Mind and Psychology, Harvester Press, Sussex, 1979.

• Hubert Dreyfus, What Computers Still Can't Do, A Critique of Artificial Reason, MIT Press, Cambridge, 1992.

  A critique of the notion that human intelligence and machine intelligence can even be compared.

• Stuart Kauffman, At Home in the Universe: The Search for Laws of Self-Organization and Complexity, Oxford University Press, Reprint Edition 1996.

  The author argues that natural selection is an important but incomplete explanation for "the crafting of the fine architectures of the biosphere, from cell to organism to ecosystem. Another source -- self-organization -- is the root source of order."

• Roger Penrose, The Emperor's New Mind, Oxford University Press, New York, 1989 (Paperback by Vintage Press, London, 1990).

  A critique of the basic assumptions and objectives underlying artificial intelligence.

• John Searle, Mind, Brains, and Science, Harvard University Press, Cambridge, Massachusetts, 1984

  Searle published his "Chinese Test" many times, in various publications. This booklet is his BBC lectures.

• Joseph Weizenbaum, Computer Power and Human Reason, W. H. Freeman and Co., San Francisco, 1976

  Key issue raised: Is it moral to engage in artificial intelligence and alife?

Miscellaneous On-Line Materials

• Leigh Tesfatsion (Economics, ISU) developed an introductory undergraduate course on Agent-Based Computational Economics (Econ 308). The syllabus for this course, available here, is organized as a self-study guide for students and long-distance learners alike. Resources available at this site (mostly on-line) include lecture notes, readings, homework exercises, student projects, and related links.

• Geoffrey M. Hodgson, Darwinism in Economics: From Analogy to Ontology (pdf,120KB), Journal of Evolutionary Economics 12 (2000), 259-281.

  Abstract: The author argues that objections to `biological analogies' and `Darwinism' put forward by several social scientists, including evolutionary economists, are ungrounded. He argues that Darwinism includes a broad theoretical framework for the analysis of the evolution of all open, complex systems, including socio-economic systems. He concludes by noting that the recognition of the relevance of Darwinism does not undermine the need for auxiliary theories and explanations in the economic domain.

• Paul Krugman, What Economists Can Learn from Evolutionary Theorists (html), Presentation, European Association for Evolutionary Political Economy, November, 1996.

  Abstract: A cautious assessment of the potential of evolutionary thinking for economic analysis. In particular, Krugman argues that evolutionary economists should not be too quick to abandon the use of equilibrium modeling since many scientists in other disciplines make use of equilibrium assumptions.

  Note by LT: A further question must be raised here, I believe. How many scientists in other disciplines follow the common practice of economic theorists of incorporating equilibrium conditions into their system descriptions as untested maintained hypotheses, without consideration of their basins of attraction and hence their likelihood of occurrence and persistence? There is nothing wrong with incorporating equilibrium assumptions once their empirical relevance has been established, but who wants to spend time studying eggs on their tip points?

• Leigh Tesfatsion (Economics, ISU) maintains an annotated list of pointers to ACE/CAS Computational Laboratories and Demonstration Software. The goal of this site is to facilitate the understanding of the ACE methodology by providing people with an opportunity to gain hands-on experience running simple ACE/CAS experiments under different parameter settings with no original programming required and with rapid visual feedback of findings.

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