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Signaling and Tacit Collusion in an Infinitely Repeated Prisoners' Dilemma

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  • Joseph E. Harrington, Jr.
  • Wei Zhao

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.

Suggested Citation

  • Joseph E. Harrington, Jr. & Wei Zhao, 2012. "Signaling and Tacit Collusion in an Infinitely Repeated Prisoners' Dilemma," Economics Working Paper Archive 587, The Johns Hopkins University,Department of Economics.
    • Handle: RePEc:jhu:papers:587
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    1. 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.
    2. 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.
    3. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-465, Autumn.
    4. Mehmet Ekmekci & Alp Atakan, 2009. "Reputations with Long Run Players," 2009 Meeting Papers 220, Society for Economic Dynamics.
    5. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    6. V. Bhaskar, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 135-149.
    7. Marina Halac, 2012. "Relational Contracts and the Value of Relationships," American Economic Review, American Economic Association, vol. 102(2), pages 750-779, April.
    8. Susan Athey & Kyle Bagwell, 2008. "Collusion With Persistent Cost Shocks," Econometrica, Econometric Society, vol. 76(3), pages 493-540, May.
    9. Sylvain Chassang, 2010. "Building Routines: Learning, Cooperation, and the Dynamics of Incomplete Relational Contracts," American Economic Review, American Economic Association, vol. 100(1), pages 448-465, March.
    10. 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.
    11. 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.
    12. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
    13. 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, May.
    14. 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.
    15. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    16. Crawford, Vincent P & Haller, Hans, 1990. "Learning How to Cooperate: Optimal Play in Repeated Coordination Games," Econometrica, Econometric Society, vol. 58(3), pages 571-595, May.
    17. Gerlach, Heiko, 2009. "Stochastic market sharing, partial communication and collusion," International Journal of Industrial Organization, Elsevier, vol. 27(6), pages 655-666, November.
    18. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
    19. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    20. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    21. Zheng, Bingyong, 2008. "Approximate efficiency in repeated games with correlated private signals," Games and Economic Behavior, Elsevier, vol. 63(1), pages 406-416, May.
    22. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    23. Joseph Farrell, 1987. "Cheap Talk, Coordination, and Entry," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 34-39, Spring.
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    Cited by:

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    2. Ronen Gradwohl & Rann Smorodinsky, 2021. "Privacy, Patience, and Protection," Dynamic Games and Applications, Springer, vol. 11(4), pages 759-784, December.
    3. Loet Stekelenburg & Peter T. Dijkstra & Elianne F. Steenbergen & Jessanne Mastop & Naomi Ellemers, 2023. "Integrating Norms, Knowledge, and Social Ties into the Deterrence Model of Cartels: A Survey Study of Business Executives," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 63(3), pages 275-315, November.
    4. Chowdhury, Subhasish M. & Crede, Carsten J., 2020. "Post-cartel tacit collusion: Determinants, consequences, and prevention," International Journal of Industrial Organization, Elsevier, vol. 70(C).
    5. Bos Iwan & Letterie Wilko & Vermeulen Dries, 2015. "Antitrust as Facilitating Factor for Collusion," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 15(2), pages 797-814, April.
    6. Tveito, Andreas, 2019. "Coordination and price leadership in an unregulated environment," Working Papers in Economics 4/19, University of Bergen, Department of Economics.
    7. Epivent, Andréa & Lambin, Xavier, 2024. "On algorithmic collusion and reward–punishment schemes," Economics Letters, Elsevier, vol. 237(C).

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