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Equal Pay for all Prisoners/ The Logic of Contrition


  • M.C. Boerlijst
  • M.A. Nowak
  • K. Sigmund


This report deals with two questions concerning the emergence of cooperative strategies in repeated games. The first part is concerned with the Perfect Folk Theorem and presents a vast class of equilibrium solutions based on Markovian strategies. Simple strategies, called equalizers, are introduced and discussed: if players adopt such strategies, the same payoff results for every opponent. The second part analyzes strategies implemented by finite automata. Such strategies are relevant in an evolutionary context; an important instance is called Contrite Tit For Tat. In populations of players adopting such strategies, Contrite Tit For Tat survives very well- at least as long as errors are restricted to mistakes in implementation ('the trembling hand'). However, this cooperative strategy cannot persist if mistakes in perception are included as well.

Suggested Citation

  • M.C. Boerlijst & M.A. Nowak & K. Sigmund, 1997. "Equal Pay for all Prisoners/ The Logic of Contrition," Working Papers ir97073, International Institute for Applied Systems Analysis.
  • Handle: RePEc:wop:iasawp:ir97073

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    References listed on IDEAS

    1. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    2. Binmore, K. & Samuelson, L., 1990. "Evolutionary Stability In Repeated Games Played By Finite Automata," Working papers 90-29, Wisconsin Madison - Social Systems.
    3. Jonathan Bendor & Roderick M. Kramer & Suzanne Stout, 1991. "When in Doubt..," Journal of Conflict Resolution, Peace Science Society (International), vol. 35(4), pages 691-719, December.
    4. Binmore, Kenneth G. & Samuelson, Larry, 1992. "Evolutionary stability in repeated games played by finite automata," Journal of Economic Theory, Elsevier, vol. 57(2), pages 278-305, August.
    5. Jonathan Bendor, 1993. "Uncertainty and the Evolution of Cooperation," Journal of Conflict Resolution, Peace Science Society (International), vol. 37(4), pages 709-734, December.
    6. Fudenberg, Drew & Maskin, Eric, 1990. "Evolution and Cooperation in Noisy Repeated Games," American Economic Review, American Economic Association, vol. 80(2), pages 274-279, May.
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    Cited by:

    1. Ethan Akin, 2015. "What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma," Games, MDPI, Open Access Journal, vol. 6(3), pages 1-16, June.
    2. Alexander J. Stewart & Joshua B. Plotkin, 2015. "The Evolvability of Cooperation under Local and Non-Local Mutations," Games, MDPI, Open Access Journal, vol. 6(3), pages 1-20, July.
    3. Hilbe, Christian & Traulsen, Arne & Sigmund, Karl, 2015. "Partners or rivals? Strategies for the iterated prisoner's dilemma," Games and Economic Behavior, Elsevier, vol. 92(C), pages 41-52.

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