IDEAS home Printed from
   My bibliography  Save this paper

Signaling and Tacit Collusion in an Infinitely Repeated Prisoners' Dilemma


  • Joseph E. Harrington, Jr.
  • Wei Zhao


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, 2010. "Signaling and Tacit Collusion in an Infinitely Repeated Prisoners' Dilemma," Economics Working Paper Archive 559, The Johns Hopkins University,Department of Economics.
  • Handle: RePEc:jhu:papers:559

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    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. Joseph E. Harrington & Andrzej Skrzypacz, 2011. "Private Monitoring and Communication in Cartels: Explaining Recent Collusive Practices," American Economic Review, American Economic Association, vol. 101(6), pages 2425-2449, October.
    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. Harrington, Joseph Jr., 1995. "Cooperation in a one-shot Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 8(2), pages 364-377.
    5. Susan Athey & Kyle Bagwell, 2008. "Collusion With Persistent Cost Shocks," Econometrica, Econometric Society, vol. 76(3), pages 493-540, May.
    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. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
    8. 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.
    9. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    10. 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.
    11. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    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. Michihiro Kandori, 1992. "Social Norms and Community Enforcement," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 63-80.
    14. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    15. Joseph Farrell, 1987. "Cheap Talk, Coordination, and Entry," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 34-39, Spring.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jhu:papers:559. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (None). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.