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Repeated Games with Frequent Signals

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  • Fudenberg, Drew
  • Levine, David

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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Bibliographic Info

Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3160491.

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Date of creation: 2009
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Publication status: Published in Quarterly Journal of Economics
Handle: RePEc:hrv:faseco:3160491

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  1. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195300796, October.
  2. Hellwig, Martin & Schmidt, Klaus M., 2001. "Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Sonderforschungsbereich 504 Publications, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim 01-52, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  3. Yuliy Sannikov & Andrzej Skrzypacz, 2007. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," American Economic Review, American Economic Association, American Economic Association, vol. 97(5), pages 1794-1823, December.
  4. David G. Pearce & Dilip Abreu & Paul R. Milgrom, 1988. "Information and Timing in Repeated Partnerships," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 875, Cowles Foundation for Research in Economics, Yale University.
  5. Klein, Benjamin & Leffler, Keith B, 1981. "The Role of Market Forces in Assuring Contractual Performance," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 89(4), pages 615-41, August.
  6. Drew Fudenberg & David K Levine, 2007. "A Large Deviation Theorem for Triangular Arrays," Levine's Working Paper Archive 814577000000000002, David K. Levine.
  7. Drew Fudenberg & David Kreps & Eric Maskin, 1988. "Repeated Games with Long-Run and Short-Run Players," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 474, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. Yuliy Sannikov & Andrzej Skrzypacz, 2006. "The role of information in repeated games with frequent actions," 2006 Meeting Papers, Society for Economic Dynamics 871, Society for Economic Dynamics.
  9. Jonathan Levin, 2000. "Relational Incentive Contracts," Working Papers, Stanford University, Department of Economics 01002, Stanford University, Department of Economics.
  10. Simon, Leo K. & Stinchcombe, Maxwell B., 1987. "Extensive From Games in Continuous Time: Pure Strategies," Department of Economics, Working Paper Series, Department of Economics, Institute for Business and Economic Research, UC Berkeley qt03x115sh, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  11. 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, Wiley Blackwell, vol. 53(1), pages 59-69, January.
  12. Eduardo Faingold & Yuliy Sannikov, 2007. "Equilibrium Degeneracy and Reputation Effects," NajEcon Working Paper Reviews 843644000000000216, www.najecon.org.
  13. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  14. Kandori, Michihiro, 1992. "The Use of Information in Repeated Games with Imperfect Monitoring," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 59(3), pages 581-93, July.
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Cited by:
  1. Feigenberg, Benjamin & Field, Erica Marie & Pande, Rohini, 2010. "Building Social Capital Through Microfinance," Scholarly Articles 4449105, Harvard 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. Osório Costa, Antonio Miguel, 2011. "A Folk Theorem for Games when Frequent Monitoring Decreases Noise," Working Papers 2072/179667, Universitat Rovira i Virgili, Department of Economics.
  4. Osório Costa, Antonio Miguel, 2011. "Public Monitoring with Uncertainty in the Time Repetitions," Working Papers 2072/179668, Universitat Rovira i Virgili, Department of Economics.
  5. Doraszelski, Ulrich & Escobar, Juan F., 2012. "Restricted feedback in long term relationships," Journal of Economic Theory, Elsevier, Elsevier, vol. 147(1), pages 142-161.
  6. Kobayashi, Hajime & Ohta, Katsunori, 2012. "Optimal collusion under imperfect monitoring in multimarket contact," Games and Economic Behavior, Elsevier, Elsevier, vol. 76(2), pages 636-647.
  7. Drew Fudenberg & David K Levine, 2013. "Tail Probabilities for Triangular Arrays," Levine's Working Paper Archive 786969000000000685, David K. Levine.
  8. 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.

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