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The optimal degree of cooperation in the repeated Prisoners' Dilemma with side payments

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  • Fong, Yuk-fai
  • Surti, Jay

Abstract

In the infinitely repeated Prisoners' Dilemma with side payments, we characterize the Pareto frontier of the set of subgame perfect equilibrium payoffs for all possible combinations of discount factors. Play paths implementing Pareto dominant equilibrium payoffs are uniquely determined in all but the first period. Full cooperation does not necessarily implement these payoffs even when it maximizes total stage game payoffs. Rather, when the difference in players' discount factors is sufficiently large, Pareto dominant equilibrium payoffs are implemented by partial cooperation supported by repeated payments from the impatient to the patient player. When both players are sufficiently patient, such payoffs, while implemented via full cooperation, are supported by repeated payments from the impatient to the patient player. We characterize conditions under which public randomization has no impact on the Pareto dominant equilibrium payoffs and conditions under which such payoffs are robust to renegotiation.

Suggested Citation

  • Fong, Yuk-fai & Surti, Jay, 2009. "The optimal degree of cooperation in the repeated Prisoners' Dilemma with side payments," Games and Economic Behavior, Elsevier, vol. 67(1), pages 277-291, September.
  • Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:277-291
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    References listed on IDEAS

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    Cited by:

    1. Goldlücke, Susanne & Kranz, Sebastian, 2013. "Renegotiation-proof relational contracts," Games and Economic Behavior, Elsevier, vol. 80(C), pages 157-178.
    2. Carmona, Guilherme & Carvalho, Luís, 2016. "Repeated two-person zero-sum games with unequal discounting and private monitoring," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 131-138.
    3. Malcolm Kass & Enrique Fatas & Catherine Eckel & Daniel Arce, 2015. "The UN in the lab," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(3), pages 625-651, October.
    4. Roman, Mihai Daniel, 2008. "Entreprises behavior in cooperative and punishment‘s repeated negotiations," MPRA Paper 37527, University Library of Munich, Germany, revised 05 Jan 2009.
    5. Kranz, Sebastian & Ohlendorf, Susanne, 2009. "Renegotiation-Proof Relational Contracts with Side Payments," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 259, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    6. David A. Miller & Joel Watson, 2013. "A Theory of Disagreement in Repeated Games With Bargaining," Econometrica, Econometric Society, vol. 81(6), pages 2303-2350, November.
    7. Sebastian Kranz, 2012. "Discounted Stochastic Games with Voluntary Transfers," Cowles Foundation Discussion Papers 1847, Cowles Foundation for Research in Economics, Yale University.
    8. Roman, Mihai Daniel, 2010. "A game theoretic approach of war with financial influences," MPRA Paper 38389, University Library of Munich, Germany.

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