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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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    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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