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Signaling and Tacit Collusion in an Infinitely Repeated Prisoners' Dilemma

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  • Joseph E. Harrington, Jr.
  • Wei Zhao
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    Abstract

    In the context of an infinitely repeated Prisoners' Dilemma, we explore how cooperation is initiated when players signal and coordinate through their actions. There are two types of players - patient and impatient - and a player's type is private information. An impatient type is incapable of cooperative play, while if both players are patient types - and this is common knowledge - then they can cooperate with a grim trigger strategy. We find that the longer that players have gone without cooperating, the lower is the probability that they'll cooperate in the next period. While the probability of cooperation emerging is always positive, there is a positive probability that cooperation never occurs.

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    Bibliographic Info

    Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 559.

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    Date of creation: Jun 2010
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    Handle: RePEc:jhu:papers:559

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    1. Crawford, Vincent P & Haller, Hans, 1990. "Learning How to Cooperate: Optimal Play in Repeated Coordination Games," Econometrica, Econometric Society, vol. 58(3), pages 571-95, May.
    2. Aoyagi, Masaki, 2002. "Collusion in Dynamic Bertrand Oligopoly with Correlated Private Signals and Communication," Journal of Economic Theory, Elsevier, vol. 102(1), pages 229-248, January.
    3. Makoto Hanazono & Huanxing Yang, 2007. "Collusion, Fluctuating Demand, And Price Rigidity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(2), pages 483-515, 05.
    4. Ichiro Obara, 2005. "Folk Theorem with Communication," UCLA Economics Online Papers 366, UCLA Department of Economics.
    5. David Kreps & Paul Milgrom & John Roberts & Bob Wilson, 2010. "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma," Levine's Working Paper Archive 239, David K. Levine.
    6. Joseph Farrell, 1987. "Cheap Talk, Coordination, and Entry," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 34-39, Spring.
    7. Joseph E. Harrington, Jr. & Andrzej Skrzypacz, 2009. "Private Monitoring and Communication in Cartels: Explaining Recent Collusive Practices," Economics Working Paper Archive 555, The Johns Hopkins University,Department of Economics.
    8. Michihiro Kandori, 2001. "Introduction to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-114, CIRJE, Faculty of Economics, University of Tokyo.
    9. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-65, Autumn.
    10. Susan Athey & Kyle Bagwell, 2004. "Collusion with Persistent Cost Shocks," Levine's Bibliography 122247000000000334, UCLA Department of Economics.
    11. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    12. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    13. Kandori, Michihiro, 1992. "Social Norms and Community Enforcement," Review of Economic Studies, Wiley Blackwell, vol. 59(1), pages 63-80, January.
    14. Zheng, Bingyong, 2008. "Approximate efficiency in repeated games with correlated private signals," Games and Economic Behavior, Elsevier, vol. 63(1), pages 406-416, May.
    15. Harrington, Joseph Jr., 1995. "Cooperation in a one-shot Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 8(2), pages 364-377.
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