IDEAS home Printed from
   My bibliography  Save this paper

Cooperation, Secret Handshakes, and Imitation in the Prisoners' Dilemma


  • Thomas Wiseman
  • Okan Yilankaya


In the prisoners' dilemma game, the only evolutionary stable strategy is defection, even though nutual cooperation yields a higher payoff. Building on a paper by Robson (1990), we introduce mutants who have the ability to send a (costly) signal, i.e., the "secret handshake," before each round of the game and to condition their actions on whether or not they observe the same signal from their opponent. A population playing the strategy "always defect" is vulnerable to secret handshake mutants who cooperate when they meet other secret handshakers and defect against tother opponents. However, these secret handshakers are in turn vulberable ot a second round of mutants who imitate the secret handshake and then defect against all opponents. But now a new group of secret handshakers with a different secret handshake can arise. Thus, play can cycle between cooperation and defection. We study the dynamics of that cycling. We show that in the limit, as the probability of mutation goes to zero, cooperation occurs on average half the time. Using simulations to study the implications of our model when the mutation probability is larger than zero, we find that it is possible for cooperation to be sustained for long periods. In general, cooperation is favored when mutual cooperation has aj large payoff advantage over mutual defection, and when the payoff advantage of unilateral defection is small. Surprisingly, however, there are cases where an increased payoff to unilateral defection actually raises the level of cooperation.

Suggested Citation

  • Thomas Wiseman & Okan Yilankaya, 1999. "Cooperation, Secret Handshakes, and Imitation in the Prisoners' Dilemma," Discussion Papers 1248, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1248

    Download full text from publisher

    File URL:
    File Function: main text
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Bergstrom, Theodore C & Stark, Oded, 1993. "How Altruism Can Prevail in an Evolutionary Environment," American Economic Review, American Economic Association, vol. 83(2), pages 149-155, May.
    2. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August.
    3. Guttman, Joel M., 1996. "Rational actors, tit-for-tat types, and the evolution of cooperation," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 27-56, January.
    4. John H. Miller & Carter Butts & David Rode, 1998. "Communication and Cooperation," Working Papers 98-04-037, Santa Fe Institute.
    5. Banerjee, Abhijit & Weibull, Jorgen W., 2000. "Neutrally Stable Outcomes in Cheap-Talk Coordination Games," Games and Economic Behavior, Elsevier, vol. 32(1), pages 1-24, July.
    6. Ockenfels, Peter, 1993. "Cooperation in prisoners' dilemma : An evolutionary approach," European Journal of Political Economy, Elsevier, vol. 9(4), pages 567-579, November.
    7. Bhaskar, V., 1998. "Noisy Communication and the Evolution of Cooperation," Journal of Economic Theory, Elsevier, vol. 82(1), pages 110-131, September.
    8. Frank, Robert H, 1987. "If Homo Economicus Could Choose His Own Utility Function, Would He Want One with a Conscience?," American Economic Review, American Economic Association, vol. 77(4), pages 593-604, September.
    9. Fudenberg, Drew & Maskin, Eric, 1990. "Evolution and Cooperation in Noisy Repeated Games," American Economic Review, American Economic Association, vol. 80(2), pages 274-279, May.
    10. Kim, Yong-Gwan & Sobel, Joel, 1995. "An Evolutionary Approach to Pre-play Communication," Econometrica, Econometric Society, vol. 63(5), pages 1181-1193, September.
    11. Nachbar, John H., 1992. "Evolution in the finitely repeated prisoner's dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 19(3), pages 307-326, December.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Mary L. Rigdon & Kevin A. McCabe & Vernon L. Smith, 2007. "Sustaining Cooperation in Trust Games," Economic Journal, Royal Economic Society, vol. 117(522), pages 991-1007, July.
    2. repec:wsi:igtrxx:v:05:y:2003:i:03:n:s0219198903001033 is not listed on IDEAS
    3. Man, Priscilla T.Y., 2012. "Efficiency and stochastic stability in normal form games," Games and Economic Behavior, Elsevier, vol. 76(1), pages 272-284.

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

    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:nwu:cmsems:1248. 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: (Fran Walker). 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.