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Equal Pay for all Prisoners/ The Logic of Contrition

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

Abstract

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

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    1. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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    3. Jonathan Bendor, 1993. "Uncertainty and the Evolution of Cooperation," Journal of Conflict Resolution, Peace Science Society (International), vol. 37(4), pages 709-734, December.
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    5. Binmore, K. & Samuelson, L., 1990. "Evolutionary Stability In Repeated Games Played By Finite Automata," Working papers 90-29, Wisconsin Madison - Social Systems.
    6. 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.
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    Cited by:

    1. Alexander J. Stewart & Joshua B. Plotkin, 2015. "The Evolvability of Cooperation under Local and Non-Local Mutations," Games, MDPI, vol. 6(3), pages 1-20, July.
    2. Matus Halas, 2018. "Balancing Against Threats In Interactions Determined By Distance And Overall Gains," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-22, August.
    3. El-Salam, Salsabeel M. Abd & El-Seidy, Essam & Abdel-Malek, Amira R., 2023. "Evaluating zero-determinant strategies’ effects on cooperation and conflict resolution in repeated games," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Kang, Kai & Tian, Jinyan & Zhang, Boyu, 2024. "Cooperation and control in asymmetric repeated games," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    5. Peter S. Park & Martin A. Nowak & Christian Hilbe, 2022. "Cooperation in alternating interactions with memory constraints," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    6. Fukutomi, Masao & Kurokawa, Shun, 2018. "How much cost should reciprocators pay in order to distinguish the opponent's cooperation from the opponent's defection?," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 301-314.
    7. Benjamin M Zagorsky & Johannes G Reiter & Krishnendu Chatterjee & Martin A Nowak, 2013. "Forgiver Triumphs in Alternating Prisoner's Dilemma," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-8, December.
    8. Martin Posch, 2001. "Win Stay, Lose Shift or Imitatation – Only the Choice of Peers Counts," Vienna Economics Papers vie0109, University of Vienna, Department of Economics.
    9. Ethan Akin, 2015. "What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma," Games, MDPI, vol. 6(3), pages 1-16, June.
    10. 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.
    11. Christian Hilbe & Martin A Nowak & Arne Traulsen, 2013. "Adaptive Dynamics of Extortion and Compliance," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-9, November.
    12. Kurokawa, Shun, 2019. "How memory cost, switching cost, and payoff non-linearity affect the evolution of persistence," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 174-192.
    13. Misato Inaba & Nobuyuki Takahashi, 2019. "Linkage Based on the Kandori Norm Successfully Sustains Cooperation in Social Dilemmas," Games, MDPI, vol. 10(1), pages 1-15, February.

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