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Informational Smallness and Private Monitoring in Repeated Games

Author

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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.

Suggested Citation

  • Richard McLean & Ichiro Obara & Andrew Postlewaite, 2001. "Informational Smallness and Private Monitoring in Repeated Games," PIER Working Paper Archive 05-024, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 20 Jul 2005.
  • Handle: RePEc:pen:papers:05-024
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Michihiro Kandori & Ichiro Obara, 2006. "Efficiency in Repeated Games Revisited: The Role of Private Strategies," Econometrica, Econometric Society, vol. 74(2), pages 499-519, March.
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    5. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    6. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273 World Scientific Publishing Co. Pte. Ltd..
    7. 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: A Long-Run Collaboration On Long-Run Games, chapter 15, pages 331-343 World Scientific Publishing Co. Pte. Ltd..
    8. Mailath, George J. & Morris, Stephen, 2006. "Coordination failure in repeated games with almost-public monitoring," Theoretical Economics, Econometric Society, vol. 1(3), pages 311-340, September.
    9. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-554, May.
    10. Luca Anderlini & Roger Lagunoff, 2005. "Communication in dynastic repeated games: ‘Whitewashes’ and ‘coverups’," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 265-299, August.
    11. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
    12. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
    13. Olivier Compte, 1998. "Communication in Repeated Games with Imperfect Private Monitoring," Econometrica, Econometric Society, vol. 66(3), pages 597-626, May.
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    Cited by:

    1. 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: A Long-Run Collaboration On Long-Run Games, chapter 15, pages 331-343 World Scientific Publishing Co. Pte. Ltd..
    2. Mailath, George J. & Morris, Stephen, 2006. "Coordination failure in repeated games with almost-public monitoring," Theoretical Economics, Econometric Society, vol. 1(3), pages 311-340, September.
    3. Wolitzky, Alexander, 2015. "Communication with tokens in repeated games on networks," Theoretical Economics, Econometric Society, vol. 10(1), January.
    4. McLean, Richard & Obara, Ichiro & Postlewaite, Andrew, 2014. "Robustness of public equilibria in repeated games with private monitoring," Journal of Economic Theory, Elsevier, vol. 153(C), pages 191-212.
    5. Wojciech Olszewski & Johannes Horner, 2008. "How Robust is the Folk Theorem with Imperfect," 2008 Meeting Papers 895, Society for Economic Dynamics.
    6. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
    7. Roman, Mihai Daniel, 2010. "A game theoretic approach of war with financial influences," MPRA Paper 38389, University Library of Munich, Germany.

    More about this item

    Keywords

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

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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