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Efficiency in a Repeated Prisoners' Dilemma with Imperfect Private Monitoring

  • Fong, Kyna
  • Sannikov, Yuliy
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    We study the repeated two-player Prisoners' Dilemma with imperfect private monitoring and no communication. Letting the discount factor go to one and holding the monitoring structure fixed, we achieve asymptotic efficiency. Unlike previous works on private monitoring, which have confined attention to signals that are either almost perfect or conditionally independent, we allow for both imperfect and correlated signals but assume that they are sufficiently private, i.e. private actions are more informative than private signals about the opponent's signals. Interestingly, for the game we study, even the existing literature that allows communication has not yet yielded efficiency.

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    Paper provided by Department of Economics, Institute for Business and Economic Research, UC Berkeley in its series Department of Economics, Working Paper Series with number qt8vz4q9tr.

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    Date of creation: 28 Feb 2007
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    Handle: RePEc:cdl:econwp:qt8vz4q9tr
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    1. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
    2. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, March.
    3. Fudenberg, Drew & Levine, David, 2007. "The Nash-Threats Folk Theorem with Communication and Approximate Common Knowledge in Two Player Games," Scholarly Articles 3203772, Harvard University Department of Economics.
    4. Hitoshi Matsushima, 2004. "Repeated Games with Private Monitoring: Two Players," Econometrica, Econometric Society, vol. 72(3), pages 823-852, 05.
    5. Dilip Abreu & Paul Milgrom & David Pearce, 1997. "Information and timing in repeated partnerships," Levine's Working Paper Archive 636, David K. Levine.
    6. George J. Mailath & Stephen Morris, 1999. "Repeated Games with Almost-Public Monitoring," Cowles Foundation Discussion Papers 1236, Cowles Foundation for Research in Economics, Yale University.
    7. V. Bhaskar & Ichiro Obara, . "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Penn CARESS Working Papers d93eb6f40c65728f9e1a7b114, Penn Economics Department.
    8. Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994. "The Folk Theorem with Imperfect Public Information," Econometrica, Econometric Society, vol. 62(5), pages 997-1039, September.
    9. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
    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. Michihiro Kandori, 2001. "Introduction to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-114, CIRJE, Faculty of Economics, University of Tokyo.
    12. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
    13. Aoyagi, Masaki, 2002. "Collusion in Dynamic Bertrand Oligopoly with Correlated Private Signals and Communication," Journal of Economic Theory, Elsevier, vol. 102(1), pages 229-248, January.
    14. Johannes Hörner & Wojciech Olszewski, 2006. "The Folk Theorem for Games with Private Almost-Perfect Monitoring," Econometrica, Econometric Society, vol. 74(6), pages 1499-1544, November.
    15. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
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