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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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  • 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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    1. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
    2. Andreoni,J. & Varian,H., 1999. "Pre-play contracting in the prisoners' dilemma," Working papers 18, Wisconsin Madison - Social Systems.
    3. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-351, March.
    4. Carmichael, H Lorne & MacLeod, W Bentley, 1997. "Gift Giving and the Evolution of Cooperation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 485-509, August.
    5. van Damme, Eric, 1989. "Renegotiation-proof equilibria in repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 47(1), pages 206-217, February.
    6. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142, World Scientific Publishing Co. Pte. Ltd..
    7. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    8. Matthew O. Jackson & Simon Wilkie, 2005. "Endogenous Games and Mechanisms: Side Payments Among Players," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 543-566.
    9. Marco Celentani & Drew Fudenberg & David K. Levine & Wolfgang Pesendorfer, 2008. "Maintaining A Reputation Against A Long-Lived Opponent," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 9, pages 163-176, World Scientific Publishing Co. Pte. Ltd..
    10. Mailath, George J. & Obara, Ichiro & Sekiguchi, Tadashi, 2002. "The Maximum Efficient Equilibrium Payoff in the Repeated Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 40(1), pages 99-122, July.
    11. Sorin, Sylvain, 1992. "Repeated games with complete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 4, pages 71-107, Elsevier.
    12. Evans, Robert & Maskin, Eric, 1989. "Efficient renegotiation--proof equilibria in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 361-369, December.
    13. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    14. Baliga, Sandeep & Evans, Robert, 2000. "Renegotiation in Repeated Games with Side-Payments," Games and Economic Behavior, Elsevier, vol. 33(2), pages 159-176, November.
    15. Friedel Bolle, 2001. "Why to Buy Your Darling Flowers: On Cooperation and Exploitation," Theory and Decision, Springer, vol. 50(1), pages 1-28, February.
    16. Ehud Lehrer & Leeat Yariv, 1999. "Repeated Games with Incomplete Information on One Side: The Case of Different Discount Factors," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 204-218, February.
    17. Barrett, Scott, 2001. "International cooperation for sale," European Economic Review, Elsevier, vol. 45(10), pages 1835-1850, December.
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    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. Susanne Goldlücke & Sebastian Kranz, 2018. "Discounted stochastic games with voluntary transfers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 235-263, July.
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    9. Suzi Kerr & Steffen Lippert & Edmund Lou, 2019. "Financial Transfers and Climate Cooperation," Working Papers 19_04, Motu Economic and Public Policy Research.
    10. Heidi Gjertsen & Theodore Groves & David A. Miller & Eduard Niesten & Dale Squires & Joel Watson, 2014. "A Contract-theoretic Model of Conservation Agreements," World Scientific Book Chapters, in: Kaddour Hadri & William Mikhail (ed.), Econometric Methods and Their Applications in Finance, Macro and Related Fields, chapter 15, pages 425-455, World Scientific Publishing Co. Pte. Ltd..
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    12. 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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