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Purification in the Infinitely Repeated Prisoner's Dilemma

  • V Bhaskar
  • George J. Mailath
  • Stephen Morris

This paper investigates the Harsanyi (1973)-purifiability of mixed strategies in the repeated prisoners' dilemma with perfect monitoring. We perturb the game so that in each period, a player receives a private payoff shock which is independently and identically distributed across players and periods. We focus on the purifiability of a class of one-period memory mixed strategy equilibria used by Ely and Valimaki (2002) in their study of the repeated prisoners' dilemma with private monitoring. We find that all such strategy profiles are not the limit of one-period memory equilibrium strategy profiles of the perturbed game, for almost all noise distributions. However, if we allow infinite memory strategies in the perturbed game, then any completely-mixed equilibrium is purifiable.

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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 321307000000000170.

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Date of creation: 15 Jul 2006
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Handle: RePEc:cla:levrem:321307000000000170
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  1. Bhaskar, V. & Obara, Ichiro, 2002. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 40-69, January.
  2. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
  3. V.V. Bhaskar, 2007. "Purification in the Infinitely-Repeated Prisoners' Dilemma," 2007 Meeting Papers 136, Society for Economic Dynamics.
  4. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," UCLA Economics Working Papers 826, UCLA Department of Economics.
  5. V. Bhaskar, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," Review of Economic Studies, Oxford University Press, vol. 65(1), pages 135-149.
  6. Jeffrey C. Ely & Johannes Horner & Wojciech Olszewski, 2003. "Belief-free Equilibria in Repeated Games," Levine's Working Paper Archive 666156000000000367, David K. Levine.
  7. repec:esx:essedp:576 is not listed on IDEAS
  8. V. Bhaskar & Eric van Damme, 1998. "Moral Hazard and Private Monitoring," Game Theory and Information 9809004, EconWPA.
  9. Stephen Morris, 2006. "Purification," Levine's Bibliography 321307000000000470, UCLA Department of Economics.
  10. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, December.
  11. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
  12. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
  13. Govindan, Srihari & Reny, Philip J. & Robson, Arthur J., 2003. "A short proof of Harsanyi's purification theorem," Games and Economic Behavior, Elsevier, vol. 45(2), pages 369-374, November.
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