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Purification in the Infinitely-Repeated Prisoners' Dilemma

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  • V. Bhaskar

    (University College London)

  • George J. Mailath

    (University of Pennsylvania)

  • Stephen Morris

    (Princeton University)

Abstract

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 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 any such strategy profile is 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. (Copyright: Elsevier)

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File URL: http://dx.doi.org/10.1016/j.red.2007.10.004
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Bibliographic Info

Article provided by Elsevier for the Society for Economic Dynamics in its journal Review of Economic Dynamics.

Volume (Year): 11 (2008)
Issue (Month): 3 (July)
Pages: 515-528

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Handle: RePEc:red:issued:07-130

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Related research

Keywords: Purification; Belief-free equilibria; Repeated games;

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References

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  1. Jeffrey C. Ely & Johannes Horner & Wojciech Olszewski, 2003. "Belief-free Equilibria in Repeated Games," Levine's Working Paper Archive 666156000000000367, David K. Levine.
  2. V. Bhaskar & George J. Mailath & Stephen Morris, 2006. "Purification in the Infinitely-Repeated Prisoners' Dilemma," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1571, Cowles Foundation for Research in Economics, Yale University.
  3. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(1), pages 70-83, January.
  4. Govindan, Srihari & Reny, Philip J. & Robson, Arthur J., 2003. "A short proof of Harsanyi's purification theorem," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(2), pages 369-374, November.
  5. Bhaskar, V. & van Damme, Eric, 2002. "Moral Hazard and Private Monitoring," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(1), pages 16-39, January.
  6. Stephen Morris, 2006. "Purification," Levine's Bibliography 321307000000000470, UCLA Department of Economics.
  7. Bhaskar, V, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(1), pages 135-49, January.
  8. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-255, CIRJE, Faculty of Economics, University of Tokyo.
  9. Jeffrey C. Ely & Juuso Valimaki, 1999. "A Robust Folk Theorem for the Prisoner's Dilemma," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1264, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, Elsevier, vol. 76(2), pages 345-361, October.
  11. Bhaskar, V. & Obara, Ichiro, 2002. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(1), pages 40-69, January.
  12. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195300796, October.
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