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Continuous Time Limits of Repeated Games with Imperfect Public Monitoring

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Author Info
Drew Fudenberg (Harvard University)
David Levine (Washington University)

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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. (Copyright: Elsevier)

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File URL: http://dx.doi.org/10.1016/j.red.2007.02.002
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Publisher Info
Article provided by Elsevier for the Society for Economic Dynamics in its journal Review of Economic Dynamics.

Volume (Year): 10 (2007)
Issue (Month): 2 (April)
Pages: 173-192
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Handle: RePEc:red:issued:06-189

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Related research
Keywords: Repeated games; Imperfect monitoring; Diffusion process; Folk theorem; Repeated moral hazard; Continuous-time limit;

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Find related papers by 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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  1. Hellwig, Martin F. & Schmidt, Klaus M., 2001. "Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Discussion Papers in Economics 22, University of Munich, Department of Economics. [Downloadable!]
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  2. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-33, November. [Downloadable!] (restricted)
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  3. Yuliy Sannikov & Andrzej Skrzypacz, 2004. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," 2004 Meeting Papers 418, Society for Economic Dynamics.
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  4. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June. [Downloadable!]
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  5. Drew Fudenberg & David K Levine & Satoru Takahashi, 2004. "Perfect Public Equilibrium When Players are Patient," Levine's Working Paper Archive 618897000000000865, David K. Levine. [Downloadable!]
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  6. Yuliy Sannikov & Andrzej Skrzypacz, 2006. "The role of information in repeated games with frequent actions," 2006 Meeting Papers 871, Society for Economic Dynamics. [Downloadable!]
  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. [Downloadable!] (restricted)
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  8. D. Fudenberg & D. K. Levine, 1994. "Efficiency and Observability with Long-Run and Short-Run Players," Levine's Working Paper Archive 627, David K. Levine. [Downloadable!]
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  9. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-28, March. [Downloadable!] (restricted)
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  10. Muller, Holger M., 2000. "Asymptotic Efficiency in Dynamic Principal-Agent Problems," Journal of Economic Theory, Elsevier, vol. 91(2), pages 292-301, April. [Downloadable!] (restricted)
  11. Fudenberg, Drew & Kreps, David M & Maskin, Eric S, 1990. "Repeated Games with Long-run and Short-run Players," Review of Economic Studies, Blackwell Publishing, vol. 57(4), pages 555-73, October. [Downloadable!] (restricted)
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