Skip to main content
SpringerLink
Log in

Game theory vs. multiple agents: The iterated prisoner's dilemma

  • Conference paper
  • First Online:
Artificial Social Systems (MAAMAW 1992)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 830))

Abstract

One of the basic problems of theoretical political science is whether cooperation will ensue in the Iterated Prisoner's Dilemma. Unfortunately, analytical game theory cannot be expected to solve this problem. An experimental approach by Axelrod has been tried out, suggesting the robustness of the renowned TIT FOR TAT strategy. However, this strategy only works in some environments and falters when occasional misunderstandings are possible.

In this article I simulate an artificial world of artificial individuals, facing a multitude of Iterated Prisoner's Dilemmas. The ones who do well survive, the others change their strategies. This simple dynamic approach reveals a surprising efficiency: Even for substantial amounts of misunderstanding the simulations do very well — and better than TIT FOR TAT.

The uncoerced cooperation that evolves is unexpectedly stable because it is composed of many different strategies, making it hard for any single contender to beat everyone. Such models provide a powerful metaphor for a pluralist society.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  • Abreu, Dilip & Ariel Rubinstein 1988: “The Structure of Nash Equilibrium in Repeated Games with Finite Automata” in Econometrica, vol. 56:6, p1259–81.

    Google Scholar 

  • Alchian, Armen 1950: “Uncertainty, Evolution and Economic Theory” in Alchian (ed): Economic Forces at Work; Indianapolis: Liberty Press 1977.

    Google Scholar 

  • Arthur, W. Brian 1990: “Positive Feedbacks in the Economy”; Scientific American, 2/90 p80–85.

    Google Scholar 

  • Axelrod, Robert 1981: “The emergence of cooperation among egoists”; American Political Science Review vol. 75, p306–318.

    Google Scholar 

  • Axelrod, Robert 1984: The evolution of cooperation; London: Penguin 1990.

    Google Scholar 

  • Axelrod, Robert 1986: “An evolutionary approach to norms”; American Political Science Review vol. 80:4 p1093–1111.

    Google Scholar 

  • Axelrod, Robert 1987: “The evolution of strategies in the Iterated Prisoner's Dilemma” in Lawrence Davis (ed): Genetic Algorithms and Simulated Annealing; London: Pitman; p32–41.

    Google Scholar 

  • Axelrod, Robert and Douglas Dion 1988: “The further evolution of cooperation”; Nature vol. 242, p1385–90.

    Google Scholar 

  • Binmore, Ken 1986: Modeling rational players I & II; Mimeo, London School of Economics; published in Economics and Philosophy, vol.3:9–55; 4:179–214; 1987.

    Google Scholar 

  • Binmore, Ken & Partha Dasgupta 1987: The economics of Bargaining; London: Basil Blackwell.

    Google Scholar 

  • Dasgupta, Partha 1989: “Applying game theory: Some theoretical considerations” in European Economic Review vol. 33, p619–24.

    Google Scholar 

  • David, Paul A. 1985: “Clio and the Economics of QWERTY” in AEA Papers and Proceedings; vol 72:2, p332–7.

    Google Scholar 

  • Elman, Jeffrey L. 1989: Representation and Structure in Connevtionist Models; CRL technical Report 8903, Center for Research in Language, University of California.

    Google Scholar 

  • Elster, Jon 1976: “Some conceptual problems in political theory” in Brian Barry (ed): Power and political theory; London: Wiley; p245–70.

    Google Scholar 

  • Elster, Jon 1989: The cement of society: A study of social order; Cambridge: Cambridge University Press.

    Google Scholar 

  • Friedman, Daniel 1991: “Evolutionary Games in Economics” in Econometrica, vol. 59:3, p637–66.

    Google Scholar 

  • Friedman, Milton 1953: “The Methodology of Positive Economics” in Milton Friedman (ed): Essays in Positive Economics, Chicago: University of Chicago Press.

    Google Scholar 

  • Fudenberg, Drew, David Levine, & Eric Maskin 1989: The folk theorem with imperfect public information; paper no. 523 from MIT.

    Google Scholar 

  • Fudenberg, Drew & Jean Tirole 1989: “Noncooperative game theory for industrial organization: An introduction and overview” in R. Schmalensee & R. D. Willig (ed): Handbook of Industrial Organization, volume I; Amsterdam: Elsevier Science Publishers, p259–327.

    Google Scholar 

  • Fudenberg, Drew & Erik Maskin 1986: “The folk theorem in repeated games with discounting or with incomplete information” in Econometrica vol. 54:3, p533–54.

    Google Scholar 

  • Fudenberg, Drew and Eric Maskin 1990: “Evolution and cooperation in noisy repeated games”; AEA Papers and Proceedings, vol. 80:2, p274–9.

    Google Scholar 

  • Hahn, F. H. 1982: “Reflections on the Invisible Hand”; Lloyd's Bank Review, vol. 144:1–21.

    Google Scholar 

  • Hahn, F. H. 1987: “Information, Dynamics and Equilibrium”; Scottish Journal of Political Economy, vol. 34:4, p321–34.

    Google Scholar 

  • Heckathorn, Douglas 1988: “Collective sanctions and the creation of prisoner's dilemma norms” in American Journal of Sociology; vol. 94:3, p535–62.

    Google Scholar 

  • Hirshleifer, Jack & Juan C. M. Coll 1988: “What Strategies Can Support the Evolutionary Emergence of Cooperation?” in Journal of Conflict Resolution, vol. 32:2, p367–98.

    Google Scholar 

  • Hume, David 1739 1740: A treatise of human nature; Lewis A. Selby-Bigge and Peter H. Nidditch (eds), Oxford: Oxford University Press 1987.

    Google Scholar 

  • Kalai, Ehud & William Stanford 1988: “Finite rationality and interpersonal complexity in repeated games” in Econometrica; vol. 56, p391–410.

    Google Scholar 

  • Kiyotaki, N. & R. Wright 1989: “On money as a medium of exchange” in Journal of Political Economy; vol. 97, p927–54.

    Google Scholar 

  • Krishna, Vijay 1987: The folk theorems for repeated games; Lecture notes for NATO/CNR Advanced Study Institute in Anacapri, Italy.

    Google Scholar 

  • Luce, R. Duncan and Howard Raiffa 1957: Games and decisions: introduction and critical survey; New York: John Wiley & Sons.

    Google Scholar 

  • Machiavelli, Niccolò 1531: The Discourses; Middlesex: Penguin 1987.

    Google Scholar 

  • Marimon, Ramon, Ellen McGrattan, & Thomas Sargent 1990: “Money as a medium of exchange in an economy with artificially intelligent agents” in Journal of Economic dynamics and Control; vol. 14, p329–73.

    Google Scholar 

  • Marwell, Gerald and Pamela Oliver 1988: “Social networks and collective action: A theory of the critical Mass”; American Journal of Sociology vol. 94:3 p502–34.

    Google Scholar 

  • Maynard Smith, John 1974: “The thory of games and the evolution of animal conflicts”; Journal of theoretical Biology vol. 47, p209–221.

    Google Scholar 

  • Maynard Smith, John 1989: Evolutionary Genetics; Oxford: Oxford University Press.

    Google Scholar 

  • Molander, Per 1985: “The optimal level of generosity in a selfish, uncertain environment”; Journal of Conflict Resolution vol. 29:4, p611–8.

    Google Scholar 

  • Mueller, Ulrich 1987: “Optimal retaliation for optimal cooperation”; Journal of Conflict Resolution vol. 31:4, p692–724.

    Google Scholar 

  • Nelson, Richard & Sidney Winter 1982: An Evolutionary Theory of Economic Change, Cambridge: Bellknap Press of Harward University.

    Google Scholar 

  • Nolfi, Stefano, Jeffrey Elman, & Domenico Parisi 1990: Learning and Evolution in Neural Networks; CRL technical report 9019; Center for Research in Language, University of California.

    Google Scholar 

  • Nowak, Martin 1990: “An Evolutionarily Stable Strategy May Be Inaccessible”; Journal of Theoretical Biology, vol 142:237–41.

    Google Scholar 

  • Nowak, Martin & Sigmund 1989: “Oscillations in the evolution of reciprocity” in Journal of Theoretical Biology, vol. 137, p21–26.

    Google Scholar 

  • Plunkett, Kim 1988: “Parallel distributed processing”; in Psyke & Logos, vol. 9:2 p307–336.

    Google Scholar 

  • Plunkett, Kim 1990: Neural Networks and Cognitive Models; 2. oct. 1990, educational note, Institute of Computer Science, University of Aarhus.

    Google Scholar 

  • Rasmusen, Eric 1990: Games and information: An introduction to game theory; Oxford: Basil Blackwell.

    Google Scholar 

  • Robson, Arthur 1990: “Efficiency in evolutionary games: Darwin, Nash and the secret handshake”; Journal of theoretical Biology vol. 144, p379–96.

    Google Scholar 

  • Rubinstein, A. 1986: “Finite Automata Play the Repeated Prisoner's Dilemma” in Econometrica, vol. 39:83–96.

    Google Scholar 

  • Rubinstein, A. 1987: “Perfect equilibrium in a bargaining model” in Binmore & Dasgupta 1987, p47–61.

    Google Scholar 

  • Rummelhart, David E. and JL McClelland 1986: Parallel distributed processing: Explorations in the microstructure of cognition; Cambridge MA: MIT Press.

    Google Scholar 

  • Schelling, Thomas C. 1960: The strategy of conflict; Cambridge MS: Harvard University Press 1980.

    Google Scholar 

  • Simon, Herbert A. 1955: “A Behavioral Model of Rational Choice”; The Quarterly Journal of Economics, vol 59, p99–118.

    Google Scholar 

  • Taylor, Michael 1982: Community, anarchy and liberty; Cambridge: Cambridge University Press.

    Google Scholar 

  • Taylor, Michael 1987: The possibility of cooperation; Cambridge: Cambridge University Press.

    Google Scholar 

  • Winter, Sidney 1975: “Optimization and Evolution in the Theory of the Firm” in R. H. Day & T. Groves (eds): Adaptive Economic Models, New York: Academic Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Political Science, University of Århus, DK-8000, Århus C, Denmark

    Bjørn Lomborg

Authors
  1. Bjørn Lomborg
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Cristiano Castelfranchi Eric Werner

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lomborg, B. (1994). Game theory vs. multiple agents: The iterated prisoner's dilemma. In: Castelfranchi, C., Werner, E. (eds) Artificial Social Systems. MAAMAW 1992. Lecture Notes in Computer Science, vol 830. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58266-5_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-58266-5_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58266-3

  • Online ISBN: 978-3-540-48589-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation