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Repeated Games with Frequent Signals

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  • Drew Fudenberg
  • David K Levine

Abstract

We study repeated games with frequent actions and frequent imperfect public signals, where the signals are aggregates of many discrete events, such as sales or tasks. The high-frequency limit of the equilibrium set depends both on the probability law governing the discrete events and on how many events are aggregated into a single signal. When the underlying events have a binomial distribution, the limit equilibria correspond to the equilibria of the associated continuous-time game with diffusion signals, but other event processes that aggregate to a diffusion limit can have a different set of limit equilibria. Thus the continuous-time game need not be a good approximation of the high-frequency limit when the underlying events have three or more possible values.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 814577000000000009.

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Date of creation: 13 Dec 2007
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Handle: RePEc:cla:levarc:814577000000000009

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References

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  1. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
  2. Yuliy Sannikov & Andrzej Skrzypacz, 2010. "The Role of Information in Repeated Games With Frequent Actions," Econometrica, Econometric Society, vol. 78(3), pages 847-882, 05.
  3. Drew Fudenberg & David Kreps & Eric Maskin, 1988. "Repeated Games with Long-Run and Short-Run Players," Working papers 474, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
  5. David G. Pearce & Dilip Abreu & Paul R. Milgrom, 1988. "Information and Timing in Repeated Partnerships," Cowles Foundation Discussion Papers 875, Cowles Foundation for Research in Economics, Yale University.
  6. Drew Fudenberg & David K Levine, 2007. "A Large Deviation Theorem for Triangular Arrays," Levine's Working Paper Archive 814577000000000002, David K. Levine.
  7. Simon, Leo K. & Stinchcombe, Maxwell B., 1987. "Extensive From Games in Continuous Time: Pure Strategies," Department of Economics, Working Paper Series qt03x115sh, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  8. 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.
  9. 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.
  10. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, October.
  11. Eduardo Faingold & Yuliy Sannikov, 2007. "Equilibrium Degeneracy and Reputation Effects," NajEcon Working Paper Reviews 843644000000000216, www.najecon.org.
  12. Klein, Benjamin & Leffler, Keith B, 1981. "The Role of Market Forces in Assuring Contractual Performance," Journal of Political Economy, University of Chicago Press, vol. 89(4), pages 615-41, August.
  13. Radner, Roy & Myerson, Roger & Maskin, Eric, 1986. "An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 59-69, January.
  14. Kandori, Michihiro, 1992. "The Use of Information in Repeated Games with Imperfect Monitoring," Review of Economic Studies, Wiley Blackwell, vol. 59(3), pages 581-93, July.
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Cited by:
  1. Feigenberg, Benjamin & Field, Erica M. & Pande, Rohini, 2010. "Building Social Capital through Microfinance," Working Paper Series rwp10-019, Harvard University, John F. Kennedy School of Government.
  2. 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.
  3. Drew Fudenberg & David K Levine, 2013. "Tail Probabilities for Triangular Arrays," Levine's Working Paper Archive 786969000000000685, David K. Levine.
  4. 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.
  5. 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.
  6. Drew Fudenberg & Yuhta Ishii & Scott Duke Kominers, 2012. "Delayed-Response Strategies in Repeated Games with Observation Lags," Levine's Working Paper Archive 786969000000000390, David K. Levine.
  7. Osório Costa, Antonio Miguel, 2011. "Public Monitoring with Uncertainty in the Time Repetitions," Working Papers 2072/179668, Universitat Rovira i Virgili, Department of Economics.
  8. Kobayashi, Hajime & Ohta, Katsunori, 2012. "Optimal collusion under imperfect monitoring in multimarket contact," Games and Economic Behavior, Elsevier, vol. 76(2), pages 636-647.
  9. Doraszelski, Ulrich & Escobar, Juan F., 2012. "Restricted feedback in long term relationships," Journal of Economic Theory, Elsevier, vol. 147(1), pages 142-161.

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