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The role of information in repeated games with frequent actions

Author

Listed:
  • Yuliy Sannikov
  • Andrzej Skrzypacz

    (GSB Stanford University)

Abstract

We show that the ways incentives can be provided during dynamic interaction depend very crucially on the manner in which players learn information. This conclusion is established in a general stationary environment with noisy public monitoring and frequent actions. The monitoring process can be represented by a sum of a multi-dimensional Brownian component and a jump process. We show that jumps can be used to provide incentives both with transfers and value burning while continuous information can be used to provide incentives only with transfers. Also, it is asymptotically optimal to use the cumulative realization of the Brownian component linearly. Additionally, we approximate the equilibrium payoff set for fixed small discount rates as the periods become short by a series of linear programming problems. These problems highlight how the two types of information can be used to provide incentives.

Suggested Citation

  • Yuliy Sannikov & Andrzej Skrzypacz, 2006. "The role of information in repeated games with frequent actions," 2006 Meeting Papers 871, Society for Economic Dynamics.
    • Handle: RePEc:red:sed006:871
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    Cited by:

    1. Bernard, Benjamin & Frei, Christoph, 2016. "The folk theorem with imperfect public information in continuous time," Theoretical Economics, Econometric Society, vol. 11(2), May.
    2. Fudenberg, Drew & Olszewski, Wojciech, 2011. "Repeated games with asynchronous monitoring of an imperfect signal," Games and Economic Behavior, Elsevier, vol. 72(1), pages 86-99, May.
    3. Pierre Yared, 2008. "The Use of Concessions in Forestalling War," 2008 Meeting Papers 32, Society for Economic Dynamics.
    4. Gregorio Curello, 2024. "Incentives for Collective Innovation," CRC TR 224 Discussion Paper Series crctr224_2024_566, University of Bonn and University of Mannheim, Germany.
    5. Christian Bayer & Klaus Waelde, 2011. "Describing the Dynamics of Distributions in Search and Matching Models by Fokker-Planck Equations," Working Papers 1110, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 21 Jul 2011.
    6. Hörner, Johannes & Takahashi, Satoru, 2016. "How fast do equilibrium payoff sets converge in repeated games?," Journal of Economic Theory, Elsevier, vol. 165(C), pages 332-359.
    7. Dirk Hackbarth & Bart Taub, 2022. "Does the Potential to Merge Reduce Competition?," Management Science, INFORMS, vol. 68(7), pages 5364-5383, July.
    8. Henri Pages & Dylan Possamaï, 2014. "A mathematical treatment of bank monitoring incentives," Finance and Stochastics, Springer, vol. 18(1), pages 39-73, January.
    9. Bhattacharya, Vivek & Manuelli, Lucas & Straub, Ludwig, 2018. "Imperfect public monitoring with a fear of signal distortion," Journal of Economic Theory, Elsevier, vol. 175(C), pages 1-37.
    10. Drew Fudenberg & David K. Levine, 2008. "Continuous time limits of repeated games with imperfect public monitoring," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 17, pages 369-388, World Scientific Publishing Co. Pte. Ltd..
    11. 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.
    12. 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.
    13. Aislinn Bohren, 2016. "Using Persistence to Generate Incentives in a Dynamic Moral Hazard Problem," PIER Working Paper Archive 16-024, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 15 Oct 2016.
    14. Staudigl, Mathias, 2014. "A limit theorem for Markov decision processes," Center for Mathematical Economics Working Papers 475, Center for Mathematical Economics, Bielefeld University.
    15. Hartman-Glaser, Barney & Piskorski, Tomasz & Tchistyi, Alexei, 2012. "Optimal securitization with moral hazard," Journal of Financial Economics, Elsevier, vol. 104(1), pages 186-202.
    16. 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.
    17. Piskorski, Tomasz & Westerfield, Mark M., 2016. "Optimal dynamic contracts with moral hazard and costly monitoring," Journal of Economic Theory, Elsevier, vol. 166(C), pages 242-281.
    18. Daehyun Kim & Ichiro Obara, 2023. "Asymptotic Value of Monitoring Structures in Stochastic Games," Papers 2308.09211, arXiv.org, revised Jul 2024.
    19. 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.
    20. Xi Chen & Yu Chen & Xuhu Wan, 2018. "Delegated Project Search," Graz Economics Papers 2018-11, University of Graz, Department of Economics.
    21. Roman, Mihai Daniel, 2010. "A game theoretic approach of war with financial influences," MPRA Paper 38389, University Library of Munich, Germany.
    22. Eduardo Faingold, 2020. "Reputation and the Flow of Information in Repeated Games," Econometrica, Econometric Society, vol. 88(4), pages 1697-1723, July.
    23. Kobayashi, Hajime & Ohta, Katsunori, 2012. "Optimal collusion under imperfect monitoring in multimarket contact," Games and Economic Behavior, Elsevier, vol. 76(2), pages 636-647.
    24. Dylan Possamai & Chiara Rossato, 2023. "Golden parachutes under the threat of accidents," Papers 2312.02101, arXiv.org, revised Dec 2024.
    25. Osório Costa, Antonio Miguel, 2011. "Public Monitoring with Uncertainty in the Time Repetitions," Working Papers 2072/179668, Universitat Rovira i Virgili, Department of Economics.

    More about this item

    Keywords

    repeated games; dynamic incentives; frequent moves;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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