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Continuous Time Limits of Repeated Games with Imperfect Public Monitoring

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  • Levine, David
  • Fudenberg, Drew

Abstract

In a repeated game with imperfect public information, the set of equilibria depends on the way that the distribution of public signals varies with the players' actions. Recent research has focused on the case of “frequent monitoring,†where the time interval between periods becomes small. Here we study a simple example of a commitment game with a long-run and short-run player in order to examine different specifications of how the signal distribution depends upon period length. We give a simple criterion for the existence of efficient equilibrium, and show that the efficiency of the equilibria that can be supported depends in an important way on the effect of the player's actions on the variance of the signals, and whether extreme values of the signals are “bad news†of “cheating†behavior, or “good news†of “cooperative†behavior.

Suggested Citation

  • Levine, David & Fudenberg, Drew, 2007. "Continuous Time Limits of Repeated Games with Imperfect Public Monitoring," Scholarly Articles 3196334, Harvard University Department of Economics.
  • Handle: RePEc:hrv:faseco:3196334
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    References listed on IDEAS

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    1. Yuliy Sannikov & Andrzej Skrzypacz, 2007. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," American Economic Review, American Economic Association, vol. 97(5), pages 1794-1823, December.
    2. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
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    4. Drew Fudenberg & David K. Levine & Satoru Takahashi, 2008. "Perfect public equilibrium when players are patient," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 16, pages 345-367 World Scientific Publishing Co. Pte. Ltd..
    5. Fudenberg Drew & Levine David K., 1994. "Efficiency and Observability with Long-Run and Short-Run Players," Journal of Economic Theory, Elsevier, vol. 62(1), pages 103-135, February.
    6. Muller, Holger M., 2000. "Asymptotic Efficiency in Dynamic Principal-Agent Problems," Journal of Economic Theory, Elsevier, vol. 91(2), pages 292-301, April.
    7. 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.
    8. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    9. Yuliy Sannikov & Andrzej Skrzypacz, 2010. "The Role of Information in Repeated Games With Frequent Actions," Econometrica, Econometric Society, vol. 78(3), pages 847-882, May.
    10. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20 World Scientific Publishing Co. Pte. Ltd..
    11. Drew Fudenberg & David M. Kreps & Eric S. Maskin, 1990. "Repeated Games with Long-run and Short-run Players," Review of Economic Studies, Oxford University Press, vol. 57(4), pages 555-573.
    12. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
    13. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    14. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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    Citations

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    Cited by:

    1. Frei, Christoph & Bernard, Benjamin, 2016. "The folk theorem with imperfect public information in continuous time," Theoretical Economics, Econometric Society, vol. 11(2), May.
    2. Staudigl, Mathias & Steg, Jan-Henrik, 2014. "On Repeated Games with Imperfect Public Monitoring: From Discrete to Continuous Time," Center for Mathematical Economics Working Papers 525, Center for Mathematical Economics, Bielefeld University.
    3. Fudenberg, Drew & Olszewski, Wojciech, 2011. "Repeated games with asynchronous monitoring of an imperfect signal," Games and Economic Behavior, Elsevier, vol. 72(1), pages 86-99, May.
    4. Pierre Yared, 2008. "The Use of Concessions in Forestalling War," 2008 Meeting Papers 32, Society for Economic Dynamics.
    5. Drew Fudenberg & David K Levine, 2013. "Tail Probabilities for Triangular Arrays," Levine's Working Paper Archive 786969000000000685, David K. Levine.
    6. repec:aea:jecper:v:31:y:2017:i:2:p:237-56 is not listed on IDEAS
    7. Yared, Pierre, 2010. "A dynamic theory of war and peace," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1921-1950, September.
    8. Osório Costa, Antonio Miguel, 2012. "The Limits of Discrete Time Repeated Games:Some Notes and Comments," Working Papers 2072/203171, Universitat Rovira i Virgili, Department of Economics.
    9. David Rahman, 2014. "The Power of Communication," American Economic Review, American Economic Association, vol. 104(11), pages 3737-3751, November.
    10. Fudenberg, Drew & Ishii, Yuhta & Kominers, Scott Duke, 2014. "Delayed-response strategies in repeated games with observation lags," Journal of Economic Theory, Elsevier, vol. 150(C), pages 487-514.
    11. Roman, Mihai Daniel, 2010. "A game theoretic approach of war with financial influences," MPRA Paper 38389, University Library of Munich, Germany.
    12. Osório, António (António Miguel), 2017. "Brownian Signals: Information Quality, Quantity and Timing in Repeated Games," Working Papers 2072/290761, Universitat Rovira i Virgili, Department of Economics.

    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • 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

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