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Purification in the Infinitely-Repeated Prisoners' Dilemma

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  • V.V. Bhaskar

Abstract

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 \cite{ElyValimaki02} 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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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2007 Meeting Papers with number 136.

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Date of creation: 2007
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Handle: RePEc:red:sed007:136

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  1. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," UCLA Economics Working Papers 826, UCLA Department of Economics.
  2. V Bhaskar & George J. Mailath & Stephen Morris, 2006. "Purification in the Infinitely Repeated Prisoner's Dilemma," Levine's Bibliography 321307000000000170, UCLA Department of Economics.
  3. Bhaskar, V. & van Damme, Eric, 2002. "Moral Hazard and Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 16-39, January.
  4. Bhaskar, V, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," Review of Economic Studies, Wiley Blackwell, vol. 65(1), pages 135-49, January.
  5. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
  6. Jeffrey Ely, 2000. "A Robust Folk Theorem for the Prisoners' Dilemma," Econometric Society World Congress 2000 Contributed Papers 0210, Econometric Society.
  7. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
  8. V. Bhaskar & Ichiro Obara, 2000. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Econometric Society World Congress 2000 Contributed Papers 1330, Econometric Society.
  9. 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.
  10. Jeffrey C. Ely & Johannes Horner & Wojciech Olszewski, 2003. "Belief-free Equilibria in Repeated Games," Levine's Working Paper Archive 666156000000000367, David K. Levine.
  11. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
  12. Stephen Morris, 2006. "Purification," Levine's Bibliography 321307000000000470, UCLA Department of Economics.
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