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Informational Smallness and Privae Momnitoring in Repeated Games, Second Version

  • Richard McLean

    ()

    (Department of Economics, Rutgers University)

  • Ichiro Obara

    ()

    (Department of Economics, UCLA)

  • Andrew Postlewaite

    ()

    (Department of Economics, University of Pennsylvania)

We consider repeated games with private monitoring that are .close. to repeated games with public/perfect monitoring. A private monitoring information structure is close to a public monitoring information structure when private signals can generate approximately the same distribution of the public signal once they are aggregated into a public signal by some public coordination device. A player.s informational size associated with the public coordination device is the key to inducing truth-telling in nearby private monitoring games when communication is possible. A player is informationally small given a public coordination device if she believes that her signal is likely to have a small impact on the public signal generated by the public coordinating device. We show that a uniformly strict equilibrium with public monitoring is robust in a certain sense: it remains an equilibrium in nearby private monitoring repeated games when the associated public coordination device, which makes private monitoring close to public monitoring, keeps every player informationally small at the same time. We also prove a new folk theorem for repeated games with private monitoring and communication by exploiting the connection between public monitoring games and private monitoring games via public coordination devices.

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File URL: http://economics.sas.upenn.edu/system/files/11-029.pdf
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Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 11-029.

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Length: 46 pages
Date of creation: 11 Apr 2005
Date of revision: 10 Feb 2011
Handle: RePEc:pen:papers:11-029
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  1. Takahashi, Satoru & Levine, David & Fudenberg, Drew, 2007. "Perfect Public Equilibrium When Players Are Patient," Scholarly Articles 3196336, Harvard University Department of Economics.
  2. Drew Fudenberg & David K Levine, 2004. "The Nash Threats Folk Theorem With Communication and Approximate Common Knowledge in Two Player Games," Levine's Working Paper Archive 618897000000000030, David K. Levine.
  3. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
  4. George J. Mailath & Stephen Morris, 2005. "Coordination Failure in Repeated Games with Almost-Public Monitoring," Levine's Bibliography 122247000000000340, UCLA Department of Economics.
  5. Hitoshi Matsushima, 2003. "Repeated Games with Private Monitoring: Two Players," CIRJE F-Series CIRJE-F-242, CIRJE, Faculty of Economics, University of Tokyo.
  6. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  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. 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.
  9. FORGES, Françoise, . "An approach to communication equilibria," CORE Discussion Papers RP -721, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," UCLA Economics Working Papers 826, UCLA Department of Economics.
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