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Signaling and tacit collusion in an infinitely repeated Prisoners’ Dilemma

  • Harrington, Joseph E.
  • Zhao, Wei
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    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 will 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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    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 64 (2012)
    Issue (Month): 3 ()
    Pages: 277-289

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    Handle: RePEc:eee:matsoc:v:64:y:2012:i:3:p:277-289
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    1. Susan Athey & Kyle Bagwell, 2004. "Collusion with Persistent Cost Shocks," Levine's Bibliography 122247000000000334, UCLA Department of Economics.
    2. V. Bhaskar & G. J. Mailath & S. Morris, 2004. "Purification in the Infinitely-Repeated Prisoners' Dilemma," Economics Discussion Papers 576, University of Essex, Department of Economics.
    3. Heiko Gerlach, 2005. "Stochastic Market Sharing, Partial Communication and Collusion," Industrial Organization 0501009, EconWPA, revised 23 Mar 2006.
    4. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    5. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
    6. 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.
    7. Michihiro Kandori, 2001. "Introduction to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-114, CIRJE, Faculty of Economics, University of Tokyo.
    8. 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.
    9. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    10. Atakan, Alp E. & Ekmekci, Mehmet, 2013. "A two-sided reputation result with long-run players," Journal of Economic Theory, Elsevier, vol. 148(1), pages 376-392.
    11. Bhaskar, V., 1994. "Informational Constraints and the Overlapping Generations Model : Folk and Anti-Folk Theorems," Discussion Paper 1994-85, Tilburg University, Center for Economic Research.
    12. Zheng, Bingyong, 2008. "Approximate efficiency in repeated games with correlated private signals," Games and Economic Behavior, Elsevier, vol. 63(1), pages 406-416, May.
    13. Pedro Dal B�, 2005. "Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games," American Economic Review, American Economic Association, vol. 95(5), pages 1591-1604, December.
    14. 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.
    15. 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.
    16. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    17. Joseph Farrell, 1987. "Cheap Talk, Coordination, and Entry," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 34-39, Spring.
    18. 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.
    19. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    20. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    21. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-65, Autumn.
    22. 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.
    23. Marina Halac, 2012. "Relational Contracts and the Value of Relationships," American Economic Review, American Economic Association, vol. 102(2), pages 750-79, April.
    24. 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.
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