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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.

Suggested Citation

  • Fudenberg, Drew & Levine, David, 2009. "Repeated Games with Frequent Signals," Scholarly Articles 3160491, Harvard University Department of Economics.
  • Handle: RePEc:hrv:faseco:3160491
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    References listed on IDEAS

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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. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
    3. 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.
    4. Simon, Leo K & Stinchcombe, Maxwell B, 1989. "Extensive Form Games in Continuous Time: Pure Strategies," Econometrica, Econometric Society, vol. 57(5), pages 1171-1214, September.
    5. Eduardo Faingold & Yuliy Sannikov, 2007. "Equilibrium Degeneracy and Reputation Effects," NajEcon Working Paper Reviews 843644000000000216, www.najecon.org.
    6. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    7. Drew Fudenberg & David M. Kreps & Eric S. Maskin, 1990. "Repeated Games with Long-run and Short-run Players," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(4), pages 555-573.
    8. 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 615-641, August.
    9. Roy Radner & Roger Myerson & Eric Maskin, 1986. "An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 59-69.
    10. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    11. Michihiro Kandori, 1992. "The Use of Information in Repeated Games with Imperfect Monitoring," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 581-593.
    12. Drew Fudenberg & Jean Tirole, 1985. "Preemption and Rent Equalization in the Adoption of New Technology," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(3), pages 383-401.
    13. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    14. Drew Fudenberg & David K Levine, 2007. "A Large Deviation Theorem for Triangular Arrays," Levine's Working Paper Archive 814577000000000002, David K. Levine.
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    Cited by:

    1. Sven Rady & Nicolas Klein & Johannes Horner, 2013. "Strongly Symmetric Equilibria in Bandit Games," 2013 Meeting Papers 1107, Society for Economic Dynamics.
    2. Staudigl, Mathias & Steg, Jan-Henrik, 2014. "On Repeated Games with Imperfect Public Monitoring: From Discrete to Continuous Time," Center for Mathematical Economics Working Papers 525, Center for Mathematical Economics, Bielefeld University.
    3. Benjamin Feigenberg & Erica M. Field & Rohini Pande, 2010. "Building Social Capital Through MicroFinance," NBER Working Papers 16018, National Bureau of Economic Research, Inc.
    4. Jan-Henrik Steg, 2018. "On Preemption in Discrete and Continuous Time," Dynamic Games and Applications, Springer, vol. 8(4), pages 918-938, December.
    5. Johannes Hörner & Nicolas Klein & Sven Rady, 2022. "Overcoming Free-Riding in Bandit Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(4), pages 1948-1992.
    6. Oberfield, Ezra & Trachter, Nicholas, 2012. "Commodity money with frequent search," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2332-2356.
    7. Drew Fudenberg & David K Levine, 2013. "Tail Probabilities for Triangular Arrays," Levine's Working Paper Archive 786969000000000685, David K. Levine.
    8. Levine, David K. & Modica, Salvatore, 2016. "Peer discipline and incentives within groups," Journal of Economic Behavior & Organization, Elsevier, vol. 123(C), pages 19-30.
    9. 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.
    10. 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.
    11. Doraszelski, Ulrich & Escobar, Juan F., 2012. "Restricted feedback in long term relationships," Journal of Economic Theory, Elsevier, vol. 147(1), pages 142-161.
    12. David Rahman, 2014. "The Power of Communication," American Economic Review, American Economic Association, vol. 104(11), pages 3737-3751, November.
    13. 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.
    14. Daehyun Kim & Ichiro Obara, 2023. "Asymptotic Value of Monitoring Structures in Stochastic Games," Papers 2308.09211, arXiv.org, revised Jul 2024.
    15. António Osório, 2018. "Brownian Signals: Information Quality, Quantity and Timing in Repeated Games," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 387-404, August.
    16. 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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