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Informational Smallness and Private Monitoring in Repeated Games

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Author Info

  • 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. George J Mailath & Stephen Morris, 2006. "Coordination Failure in Repeated Games with Almost-Public Monitoring," Levine's Bibliography 122247000000001105, UCLA Department of Economics.
  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, Harvard - Institute of Economic Research 1961, Harvard - Institute of Economic Research.
  3. Michihiro Kandori & Ichiro Obara, 2004. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Levine's Bibliography 122247000000000055, UCLA Department of Economics.
  4. George J Mailath & Stephen Morris, 2001. "Repeated Games with Almost-Public Monitoring," NajEcon Working Paper Reviews, www.najecon.org 625018000000000257, www.najecon.org.
  5. Ben-Porath, Elchanan & Kahneman, Michael, 1996. "Communication in Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, Elsevier, vol. 70(2), pages 281-297, August.
  6. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 597-626, May.
  7. Luca Anderlini & Roger Lagunoff, 2000. "Communication in Dynastic Repeated Games: `Whitewashes' and `Coverups," Working Papers, Georgetown University, Department of Economics gueconwpa~01-01-03, Georgetown University, Department of Economics, revised 01 Jul 2001.
  8. Robert J. Aumann & Lloyd S. Shapley, 1992. "Long Term Competition-A Game Theoretic Analysis," UCLA Economics Working Papers, UCLA Department of Economics 676, UCLA Department of Economics.
  9. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine.
  10. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, Econometric Society, vol. 54(3), pages 533-54, May.
  11. Richard McLean & Andrew Postlewaite, . "Informational Size and Incentive Compatibility," CARESS Working Papres, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences 99-14, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  12. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, Elsevier, vol. 21(1), pages 1-9, August.
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Cited by:
  1. 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, Harvard - Institute of Economic Research 1961, Harvard - Institute of Economic Research.
  2. Ichiro Obara, 2007. "Folk Theorem with Communication," Levine's Bibliography 784828000000000351, UCLA Department of Economics.
  3. Wolitzky, Alexander, 0. "Communication with tokens in repeated games on networks," Theoretical Economics, Econometric Society, Econometric Society.
  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. Roman, Mihai Daniel, 2010. "A game theoretic approach of war with financial influences," MPRA Paper 38389, University Library of Munich, Germany.
  6. Wojciech Olszewski & Johannes Horner, 2008. "How Robust is the Folk Theorem with Imperfect," 2008 Meeting Papers 895, Society for Economic Dynamics.

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