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Evolution and Information in a Prisoner's Dilemma Game

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  • Phillip Johnson
  • David K Levine
  • Wolfgang Pesendorfer

Abstract

In an environment of anonymous random matching, Kandori [1992] showed that with a sufficiently rich class of simple information systems the folk theorem holds. We specialize to the Prisoner's Dilemma and examine the stochastic stability of a process of learning and evolution in this setting. If the benefit of future cooperation is too small, then there is no cooperation. When the benefit of cooperation is large then only cooperation will survive in the very long run.
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  • Phillip Johnson & David K Levine & Wolfgang Pesendorfer, 1998. "Evolution and Information in a Prisoner's Dilemma Game," Levine's Working Paper Archive 2138, David K. Levine.
    • Handle: RePEc:cla:levarc:2138
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    File URL: http://www.dklevine.com/PAPERS/evo47rc.pdf
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    References listed on IDEAS

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    1. Peyton Young, H. & Foster, Dean, 1991. "Cooperation in the long-run," Games and Economic Behavior, Elsevier, vol. 3(1), pages 145-156, February.
    2. Glenn Ellison, 1994. "Cooperation in the Prisoner's Dilemma with Anonymous Random Matching," Review of Economic Studies, Oxford University Press, vol. 61(3), pages 567-588.
    3. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    4. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
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    7. 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.
    8. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
    9. Drew Fudenberg & David K. Levine, 2009. "Learning and Equilibrium," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 385-420, May.
    10. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    11. Peyton Young & Dean Foster, 2010. "Cooperation in the Short and in the Long Run," Levine's Working Paper Archive 494, David K. Levine.
    12. Monderer, Dov & Samet, Dov & Sela, Aner, 1997. "Belief Affirming in Learning Processes," Journal of Economic Theory, Elsevier, vol. 73(2), pages 438-452, April.
    13. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    14. Michihiro Kandori, 1992. "Social Norms and Community Enforcement," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 63-80.
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