Cooperation, Secret Handshakes, and Imitation in the Prisoners' Dilemma
AbstractIn 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.
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Bibliographic InfoPaper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1248.
Date of creation: Jan 1999
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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Web page: http://www.kellogg.northwestern.edu/research/math/
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Other versions of this item:
- Wiseman, Thomas & Yilankaya, Okan, 2001. "Cooperation, Secret Handshakes, and Imitation in the Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 37(1), pages 216-242, October.
- 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
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- Man, Priscilla T.Y., 2012. "Efficiency and stochastic stability in normal form games," Games and Economic Behavior, Elsevier, vol. 76(1), pages 272-284.
- Mary L. Rigdon & Kevin A. McCabe & Vernon L. Smith, 2007.
"Sustaining Cooperation in Trust Games,"
Royal Economic Society, vol. 117(522), pages 991-1007, 07.
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