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Informational Smallness and Private Monitoring in Repeated Games

  • Richard McLean


    (Department of Economics, Rutgers University)

  • Ichiro Obara


    (Department of Economics, UCLA)

  • Andrew Postlewaite


    (Department of Economics, University of Pennsylvania)

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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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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  1. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
  2. Luca Anderlini & Roger Lagunoff, 2000. "Communication in Dynastic Repeated Games: 'Whitewashes' and 'Coverups'," Working Papers gueconwpa~01-01-03, Georgetown University, Department of Economics, revised 01 Jul 2001.
  3. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
  4. Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994. "The Folk Theorem with Imperfect Public Information," Econometrica, Econometric Society, vol. 62(5), pages 997-1039, September.
  5. George J Mailath & Stephen Morris, 2001. "Repeated Games with Almost-Public Monitoring," Levine's Working Paper Archive 625018000000000257, David K. Levine.
  6. 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.
  7. 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.
  8. Stephen Morris & George J Mailath, 2005. "Coordination Failure in Repeated Games with Almost-Public Monitoring," 2005 Meeting Papers 25, Society for Economic Dynamics.
  9. Michihiro Kandori & Ichiro Obara, 2003. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," UCLA Economics Working Papers 826, UCLA Department of Economics.
  10. 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.
  11. Robert J. Aumann & Lloyd S. Shapley, 2013. "Long Term Competition -- A Game-Theoretic Analysis," Annals of Economics and Finance, Society for AEF, vol. 14(2), pages 627-640, November.
  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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