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Informational Smallness and Private Monitoring in Repeated Games

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  • Richard McLean

    ()
    (Department of Economics, Rutgers University)

  • Ichiro Obara

    ()
    (Department of Economics, UCLA)

  • Andrew Postlewaite

    ()
    (Department of Economics, University of Pennsylvania)

Abstract

For repeated games with noisy private monitoring and communication, we examine robustness of perfect public equilibrium/subgame perfect equilibrium when private monitoring is "close" to some public monitoring. Private monitoring is "close" to public monitoring if the private signals can generate approxi-mately the same public signal once they are aggregated. Two key notions on private monitoring are introduced: Informational Smallness and Distributional Variability. A player is informationally small if she believes that her signal is likely to have a small impact when private signals are aggregated to generate a public signal. Distributional variability measures the variation in a player’s conditional beliefs over the generated public signal as her private signal varies. When informational size is small relative to distributional variability (and private signals are sufficiently close to public monitoring), a uniformly strict equilibrium with public monitoring remains an equilibrium with private monitoring and communication. To demonstrate that uniform strictness is not overly restrictive, we prove a uniform folk theorem with public monitoring which, combined with our robustness result, yields a new folk theorem for repeated games with private monitoring and communication.

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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 05-024.

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Length: 35 pages
Date of creation: 01 May 2001
Date of revision: 20 Jul 2005
Handle: RePEc:pen:papers:05-024

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Keywords: Communication; Informational size; Perfect Public Equilibrium; Private monitoring; Public monitoring; Repeated games; Robustness;

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References

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  1. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine.
  2. Drew Fudenberg & David K. Levine, 2002. "The Nash Threats Folk Theorem With Communication and Approximate Common Knowledge In Two Player Games," Harvard Institute of Economic Research Working Papers 1961, Harvard - Institute of Economic Research.
  3. George J. Mailath & Stephen Morris, 2004. "Coordination Failure in Repeated Games with Almost-Public Monitoring," PIER Working Paper Archive 05-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 23 Mar 2005.
  4. Ben-Porath, Elchanan & Kahneman, Michael, 1996. "Communication in Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 70(2), pages 281-297, August.
  5. Richard McLean & Andrew Postlewaite, . "Informational Size and Incentive Compatibility," Penn CARESS Working Papers 7f6ff09d59945e06909ce4fa4, Penn Economics Department.
  6. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," CIRJE F-Series CIRJE-F-255, CIRJE, Faculty of Economics, University of Tokyo.
  7. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
  8. George J Mailath & Stephen Morris, 1999. "Repeated Games with Almost Public Monitoring," Levine's Working Paper Archive 2107, David K. Levine.
  9. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  10. Luca Anderlini & Roger Lagunoff, 2001. " Communication in Dynastic Repeated Games: `Whitewashes' and `Coverups' ," Game Theory and Information 0107001, EconWPA.
  11. Robert J. Aumann & Lloyd S. Shapley, 1992. "Long Term Competition-A Game Theoretic Analysis," UCLA Economics Working Papers 676, UCLA Department of Economics.
  12. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
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Cited by:
  1. 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.
  2. George J. Mailath & Stephen Morris, 2004. "Coordination Failure in Repeated Games with Almost-Public Monitoring," Cowles Foundation Discussion Papers 1479R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2005.
  3. Ichiro Obara, 2005. "Folk Theorem with Communication," UCLA Economics Online Papers 366, UCLA Department of Economics.
  4. Wolitzky, Alexander, 0. "Communication with tokens in repeated games on networks," Theoretical Economics, Econometric Society.
  5. Wojciech Olszewski & Johannes Horner, 2008. "How Robust is the Folk Theorem with Imperfect," 2008 Meeting Papers 895, Society for Economic Dynamics.
  6. Roman, Mihai Daniel, 2010. "A game theoretic approach of war with financial influences," MPRA Paper 38389, University Library of Munich, Germany.

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