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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.

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Bibliographic Info

Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3196334.

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Date of creation: 2007
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Publication status: Published in Review of Economic Dynamics
Handle: RePEc:hrv:faseco:3196334

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  1. D. Fudenberg & D. M. Kreps & E. Maskin, 1998. "Repeated Games with Long-run and Short-run Players," Levine's Working Paper Archive 608, David K. Levine.
  2. Dilip Abreu & Paul Milgrom & David Pearce, 1997. "Information and timing in repeated partnerships," Levine's Working Paper Archive 636, David K. Levine.
  3. Drew Fudenberg & David K. Levine & Satoru Takahashi, 2004. "Perfect Public Equilibrium When Players Are Patient," Harvard Institute of Economic Research Working Papers 2051, Harvard - Institute of Economic Research.
  4. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
  5. Muller, Holger M., 2000. "Asymptotic Efficiency in Dynamic Principal-Agent Problems," Journal of Economic Theory, Elsevier, vol. 91(2), pages 292-301, April.
  6. Martin F. Hellwig & Klaus M. Schmidt, 2002. "Discrete-Time Approximations of the Holmstrom-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Econometrica, Econometric Society, vol. 70(6), pages 2225-2264, November.
  7. Fudenberg, Drew & Levine, David, 1983. "Subgame-perfect equilibria of finite- and infinite-horizon games," Journal of Economic Theory, Elsevier, vol. 31(2), pages 251-268, December.
  8. 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.
  9. Levine, David & Fudenberg, Drew, 1994. "Efficiency and Observability with Long-Run and Short-Run Players," Scholarly Articles 3203774, Harvard University Department of Economics.
  10. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-28, March.
  11. Fudenberg, D. & Levine, D.K. & Maskin, E., 1989. "The Folk Theorem With Inperfect Public Information," Working papers 523, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. Yuliy Sannikov & Andrzej Skrzypacz, 2006. "The role of information in repeated games with frequent actions," 2006 Meeting Papers 871, Society for Economic Dynamics.
  13. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, September.
  14. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
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Cited by:
  1. Osório António M., 2012. "A Folk Theorem for Games when Frequent Monitoring Decreases Noise," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-27, April.
  2. Roman, Mihai Daniel, 2010. "A game theoretic approach of war with financial influences," MPRA Paper 38389, University Library of Munich, Germany.
  3. Yared, Pierre, 2010. "A dynamic theory of war and peace," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1921-1950, September.
  4. 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.
  5. Drew Fudenberg & David K Levine, 2013. "Tail Probabilities for Triangular Arrays," Levine's Working Paper Archive 786969000000000685, David K. Levine.
  6. Fudenberg, Drew & Ishii, Yuhta & Kominers, Scott Duke, 2014. "Delayed-response strategies in repeated games with observation lags," Scholarly Articles 11880354, Harvard University Department of Economics.
  7. 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.
  8. Osório Costa, Antonio Miguel, 2011. "Public Monitoring with Uncertainty in the Time Repetitions," Working Papers 2072/179668, Universitat Rovira i Virgili, Department of Economics.

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