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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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  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. Martin F. Hellwig & Klaus M. Schmidt, 2002. "Discrete-Time Approximations of the Holmstrom-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Econometrica, Econometric Society, Econometric Society, vol. 70(6), pages 2225-2264, November.
  3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  4. Fudenberg, Drew & Kreps, David M & Maskin, Eric S, 1990. "Repeated Games with Long-run and Short-run Players," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(4), pages 555-73, October.
  5. Yuliy Sannikov & Andrzej Skrzypacz, 2010. "The Role of Information in Repeated Games With Frequent Actions," Econometrica, Econometric Society, Econometric Society, vol. 78(3), pages 847-882, 05.
  6. Drew Fudenberg & David K Levine, 2007. "A Large Deviation Theorem for Triangular Arrays," Levine's Working Paper Archive 814577000000000002, David K. Levine.
  7. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195300796, October.
  8. 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.
  9. 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.
  10. 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.
  11. Eduardo Faingold & Yuliy Sannikov, 2007. "Equilibrium Degeneracy and Reputation Effects," NajEcon Working Paper Reviews 843644000000000216, www.najecon.org.
  12. 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.
  13. Jonathan Levin, 2000. "Relational Incentive Contracts," Working Papers, Stanford University, Department of Economics 01002, Stanford University, Department of Economics.
  14. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1713-33, November.
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Cited by:
  1. Doraszelski, Ulrich & Escobar, Juan F., 2012. "Restricted feedback in long term relationships," Journal of Economic Theory, Elsevier, vol. 147(1), pages 142-161.
  2. 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.
  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. Drew Fudenberg & David K Levine, 2013. "Tail Probabilities for Triangular Arrays," Levine's Working Paper Archive 786969000000000685, David K. Levine.
  5. 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.
  6. 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.
  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.

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