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Spatial Evolution of Automata in the Prisoners' Dilemma

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  • Kirchkamp, Oliver

Abstract

This paper applies the idea of evolution to a spatial model. We assume that prisoners' dilemmas or coordination games are played repeatedly within neighborhoods where players do not optimize but instead copy successful strategies. 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 cooperation persists even in a stochastic environment, that players do not always coordinate on risk dominant equilibria in 2 x 2 coordination games and that success among surviving strategies may differ. We also present two analytical models that explain some of these phenomena.

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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 330.

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Length: pages
Date of creation: Oct 1995
Date of revision:
Handle: RePEc:bon:bonsfb:330

Contact details of provider:
Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

Related research

Keywords: Evolutionary Game Theory; Networks; Prisoner's Dilemma; Coordination Games; Overlapping Generations;

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References

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  1. Stanley, E.A. & Ashlock, Daniel & Tesfatsion, Leigh, 1994. "Iterated Prisoner's Dilemma with Choice and Refusal of Partners," Staff General Research Papers 11180, Iowa State University, Department of Economics.
  2. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May.
  3. 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 157-79, March.
  4. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  5. 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, December.
  6. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  7. Oliver Kirchkamp, 1994. "Spatial Evolution of Automata in the Prisoners' Dilemma," Game Theory and Information 9403003, EconWPA, revised 18 May 1994.
  8. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  9. repec:att:wimass:9612 is not listed on IDEAS
  10. Eshel, I. & Samuelson, L. & Shaked, A., 1996. "Altruists, Egoists and Hooligans in a Local Interaction Model," Working papers 9612r, Wisconsin Madison - Social Systems.
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Citations

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Cited by:
  1. Kirchkamp, Oliver, 2000. "Spatial evolution of automata in the prisoners' dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 43(2), pages 239-262, October.
  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. Kirchkamp, Oliver, 1996. "Simultaneous Evolution of Learning Rules and Strategies," Discussion Paper Serie B 379, University of Bonn, Germany.
  4. Robert Hoffmann, 2001. "Social Cognition in the Evolutionary Chicken Game," Occasional Papers 2, Industrial Economics Division, revised 10 Apr 2001.
  5. 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.
  6. M.G. Zimmermann, V. M. Eguiluz, 2001. "Evolution of Cooperative Networks and the Emergence of Leadership," Computing in Economics and Finance 2001 171, Society for Computational Economics.
  7. Oliver Kirchkamp, 1995. "Asynchronous Evolution of Pairs - How spatial evolution leads to inequality," Game Theory and Information 9510004, EconWPA.
  8. Tomas Klos, . "Decentralized Interaction and Co-adaptation in the Repeated Prisoner's Dilemma," Computing in Economics and Finance 1997 88, Society for Computational Economics.
  9. Ludo Waltman & Nees Eck & Rommert Dekker & Uzay Kaymak, 2013. "An Evolutionary Model of Price Competition Among Spatially Distributed Firms," Computational Economics, Society for Computational Economics, vol. 42(4), pages 373-391, December.
  10. Jurjen Kamphorst & Gerard van der Laan, 2006. "Learning in a Local Interaction Hawk-Dove Game," Tinbergen Institute Discussion Papers 06-034/1, Tinbergen Institute.
  11. 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.
  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.
  13. Jurjen Kamphorst & Gerard van der Laan, 2006. "Learning in a Local Interaction Hawk-Dove Game," Tinbergen Institute Discussion Papers 06-034/1, Tinbergen Institute.
  14. 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.

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