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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.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 67 (2009)
Issue (Month): 1 (September)
Pages: 277-291

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Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:277-291

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Repeated Prisoners' Dilemma Side payments Differential time preferences Pareto dominant equilibrium payoffs Renegotiation-proofness;

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Cited by:
  1. 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.
  2. Sebastian Kranz, 2012. "Discounted Stochastic Games with Voluntary Transfers," Cowles Foundation Discussion Papers 1847, Cowles Foundation for Research in Economics, Yale University.
  3. 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.

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