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Efficiency in a Repeated Prisoners' Dilemma with Imperfect Private Monitoring

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  • Fong, Kyna
  • Sannikov, Yuliy

Abstract

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.

Suggested Citation

  • Fong, Kyna & Sannikov, Yuliy, 2007. "Efficiency in a Repeated Prisoners' Dilemma with Imperfect Private Monitoring," Department of Economics, Working Paper Series qt8vz4q9tr, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    • Handle: RePEc:cdl:econwp:qt8vz4q9tr
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    References listed on IDEAS

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    1. 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.
    2. Drew Fudenberg & David K. Levine, 2008. "The Nash-threats folk theorem with communication and approximate common knowledge in two player games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 15, pages 331-343, World Scientific Publishing Co. Pte. Ltd..
    3. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    4. Hitoshi Matsushima, 2004. "Repeated Games with Private Monitoring: Two Players," Econometrica, Econometric Society, vol. 72(3), pages 823-852, May.
    5. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    6. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
    7. 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.
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    11. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, March.
    12. 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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    14. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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    Cited by:

    1. Chen, Bo, 2010. "A belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring," Journal of Economic Theory, Elsevier, vol. 145(1), pages 402-420, January.

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