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Spatial Evolution of Automata in the Prisoners' Dilemma

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  • Oliver Kirchkamp

    (University of Bonn)

Abstract

The paper applies the idea of evolution to a spatial model. We assume that the prisoners' dilemma is played only within a neighborhood and that evolutionary pressure works also only on a local level. Discriminatory behavior of players is introduced representing strategies as small automata, identical for a player but possibly in different states against different neighbors. Extensive simulations show that success among surviving strategies may differ and that in contrast to undiscriminative behavior cooperation persists even in a stochastic environment. Keywords: Evolutionary Game Theory, Networks, Prisoners' Dilemma, Overlapping Generations. JEL-Code: C63, C73, D62, D83, R12, R13.

Suggested Citation

  • Oliver Kirchkamp, 1994. "Spatial Evolution of Automata in the Prisoners' Dilemma," Game Theory and Information 9403003, University Library of Munich, Germany, revised 31 Oct 1995.
  • Handle: RePEc:wpa:wuwpga:9403003
    Note: 37 pages, postscript, also available as http://witch.econ3.uni-bonn.de/~oliver/spatEvol.shtml. Hardcopy requests to kirchkamp@witch.econ3.uni-bonn.de
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384.
    2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    3. Eshel, I. & Samuelson, L. & Shaked, A., 1996. "Altruists, Egoists and Hooligans in a Local Interaction Model," Working papers 9612r, Wisconsin Madison - Social Systems.
    4. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    5. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-493, May.
    6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    7. Stanley, E.A. & Ashlock, Daniel & Tesfatsion, Leigh, 1994. "Iterated Prisoner's Dilemma with Choice and Refusal of Partners," Staff General Research Papers Archive 11180, Iowa State University, Department of Economics.
    8. Eshel, Ilan & Samuelson, Larry & Shaked, Avner, 1998. "Altruists, Egoists, and Hooligans in a Local Interaction Model," American Economic Review, American Economic Association, vol. 88(1), pages 157-179, March.
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    Cited by:

    1. Siegfried Berninghaus & Hans Haller & Alexander Outkin, 2006. "Neural networks and contagion," Revue d'économie industrielle, De Boeck Université, vol. 0(2), pages 11-11.
    2. Takács, Károly, 2010. "Hálózati kísérletek
      [Network experiments]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(11), pages 958-979.
    3. Berninghaus, Siegfried & Haller, Hans, 2007. "Pairwise interaction on random graphs," Papers 06-16, Sonderforschungsbreich 504.
    4. Robert Hoffmann, 2001. "Social Cognition in the Evolutionary Chicken Game," Occasional Papers 2, Industrial Economics Division, revised 10 Apr 2001.
    5. Dorofeenko, Victor & Shorish, Jamsheed, 2005. "Partial differential equation modelling for stochastic fixed strategy distributed systems," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 335-367, January.
    6. Robert Hoffmann, 1999. "The Independent Localisations of Interaction and Learning in the Repeated Prisoner's Dilemma," Theory and Decision, Springer, vol. 47(1), pages 57-72, August.
    7. Ludo Waltman & Nees Eck & Rommert Dekker & Uzay Kaymak, 2013. "An Evolutionary Model of Price Competition Among Spatially Distributed Firms," Computational Economics, Springer;Society for Computational Economics, vol. 42(4), pages 373-391, December.
    8. Bernd-O. Heine & Matthias Meyer & Oliver Strangfeld, 2005. "Stylised Facts and the Contribution of Simulation to the Economic Analysis of Budgeting," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 8(4), pages 1-4.
    9. Andreas Flache & Rainer Hegselmann, 1998. "Understanding Complex Social Dynamics: a Plea for Cellular Automata Based Modelling," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 1(3), pages 1-1.
    10. Oliver Kirchkamp, 1995. "Asynchronous Evolution of Pairs - How spatial evolution leads to inequality," Game Theory and Information 9510004, University Library of Munich, Germany.
    11. Bissey, Marie-Edith & Ortona, Guido, 2002. "A simulative frame to study the integration of defectors in a cooperative setting," POLIS Working Papers 24, Institute of Public Policy and Public Choice - POLIS.
    12. Kirchkamp, Oliver & Nagel, Rosemarie, 2007. "Naive learning and cooperation in network experiments," Games and Economic Behavior, Elsevier, vol. 58(2), pages 269-292, February.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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