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Cooperation, but no reciprocity: Individual strategies in the repeated Prisoner's Dilemma

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  • Breitmoser, Yves

Abstract

A recent advance in our understanding of repeated PDs is the detection of a threshold d* at which laboratory subjects start to cooperate predictively. This threshold is substantially above the classic threshold "existence of Grim equilibrium" and has been characterized axiomatically by Blonski, Ockenfels, and Spagnolo (2011, BOS). In this paper, I derive its behavioral foundations. First, I show that the threshold is equivalent to existence of a "Semi-Grim" equilibrium s_cc>s_cd=s_dc>s_dd. It is cooperative (s_cc>0.5), non-reciprocal (s_cd=s_dc), and robust to imperfect monitoring ("belief-free"). Next, I show that the no-reciprocity condition s_cd=s_dc also follows from robustness to random-utility perturbations (logit equilibrium). Finally, I re-analyze strategies in four recent experiments and find that the majority of subjects indeed plays Semi-Grim when it is an equilibrium strategy, which explains d*'s predictive success.

Suggested Citation

  • Breitmoser, Yves, 2012. "Cooperation, but no reciprocity: Individual strategies in the repeated Prisoner's Dilemma," MPRA Paper 41731, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:41731
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    References listed on IDEAS

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    Cited by:

    1. Yutaka Kayaba & Hitoshi Matsushima & Tomohisa Toyama, 2016. "Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring:Experiments and Theory," CIRJE F-Series CIRJE-F-1004, CIRJE, Faculty of Economics, University of Tokyo.
    2. Breitmoser, Yves & Valasek, Justin, 2017. "A rationale for unanimity in committees," Discussion Papers, Research Unit: Economics of Change SP II 2017-308, Social Science Research Center Berlin (WZB).
    3. Nicklisch, Andreas & Köke, Sonja & Lange, Andreas, 2016. "Is Adversity a School of Wisdom? Experimental Evidence on Cooperative Protection Against Stochastic Losses," Annual Conference 2016 (Augsburg): Demographic Change 145716, Verein für Socialpolitik / German Economic Association.
    4. Johnsen, Åshild Auglænd, 2017. "Conspiracy against the public - an experiment on collusion," Working Paper Series 03-2017, Norwegian University of Life Sciences, School of Economics and Business.
    5. Yutaka Kayaba & Hitoshi Matsushima & Tomohisa Toyama, 2017. "Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring: Experiments and Theory (Revised version of F-381)," CARF F-Series CARF-F-414, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. repec:eee:eecrev:v:104:y:2018:i:c:p:185-219 is not listed on IDEAS

    More about this item

    Keywords

    Repeated Prisoner's Dilemma; experiment; equilibrium selection; cooperative behavior; reciprocity; belief-free equilibria; robustness;

    JEL classification:

    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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