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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 587.

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    Date of creation: Feb 2012
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    Handle: RePEc:jhu:papers:587

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    1. Cripps, Martin W. & Dekel, Eddie & Pesendorfer, Wolfgang, 2005. "Reputation with equal discounting in repeated games with strictly conflicting interests," Journal of Economic Theory, Elsevier, vol. 121(2), pages 259-272, April.
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    3. 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.
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    8. Bhaskar, V., 1994. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," Papers 9485, Tilburg - Center for Economic Research.
    9. 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.
    10. Sylvain Chassang, 2010. "Building Routines: Learning, Cooperation, and the Dynamics of Incomplete Relational Contracts," American Economic Review, American Economic Association, vol. 100(1), pages 448-65, March.
    11. Mehmet Ekmekci & Alp Atakan, 2009. "Reputations with Long Run Players," 2009 Meeting Papers 220, Society for Economic Dynamics.
    12. Mehmet Ekmekci & Alp Atakan, 2009. "A two Sided Reputation Result with Long Run Players," Discussion Papers 1510, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Susan Athey & Kyle Bagwell, 1999. "Optimal Collusion with Private Information," Working papers 99-17, Massachusetts Institute of Technology (MIT), Department of Economics.
    14. Cripps, Martin W. & Thomas, Jonathan P., 1997. "Reputation and Perfection in Repeated Common Interest Games," Games and Economic Behavior, Elsevier, vol. 18(2), pages 141-158, February.
    15. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
    16. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    17. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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