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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. Fudenberg, Drew & Levine, David K., 2007. "The Nash-threats folk theorem with communication and approximate common knowledge in two player games," Journal of Economic Theory, Elsevier, vol. 132(1), pages 461-473, January.
    2. George Mailath & Stephen Morris, . ""Repeated Games with Almost-Public Monitoring''," CARESS Working Papres 99-09, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
    3. Johannes Horner & Wojciech Olszewski, 2005. "The Folk Theorem for Games with Private, Almost-Perfect Monitoring," NajEcon Working Paper Reviews 172782000000000006, www.najecon.org.
    4. Hitoshi Matsushima, 2004. "Repeated Games with Private Monitoring: Two Players," Econometrica, Econometric Society, vol. 72(3), pages 823-852, 05.
    5. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
    6. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine.
    7. Dilip Abreu & Paul Milgrom & David Pearce, 1997. "Information and timing in repeated partnerships," Levine's Working Paper Archive 636, David K. Levine.
    8. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, 03.
    9. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, March.
    10. 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.
    11. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
    12. Michihiro Kandori, 2001. "Introduction to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-114, CIRJE, Faculty of Economics, University of Tokyo.
    13. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
    14. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
    15. 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.
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