IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/525.html
   My bibliography  Save this paper

On Repeated Games with Imperfect Public Monitoring: From Discrete to Continuous Time

Author

Listed:
  • Staudigl, Mathias

    (Center for Mathematical Economics, Bielefeld University)

  • Steg, Jan-Henrik

    (Center for Mathematical Economics, Bielefeld University)

Abstract

Motivated by recent path-breaking contributions in the theory of repeated games in continuous time, this paper presents a family of discrete-time games which provides a consistent discrete-time approximation of the continuous-time limit game. Using probabilistic arguments, we prove that continuous-time games can be defined as the limit of a sequence of discrete-time games. Our convergence analysis reveals various intricacies of continuous-time games. First, we demonstrate the importance of correlated strategies in continuous-time. Second, we attach a precise meaning to the statement that a sequence of discrete-time games can be used to approximate a continuous-time game.

Suggested Citation

  • 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.
    • Handle: RePEc:bie:wpaper:525
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2698781/2902680
    File Function: First Version, 2014
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Drew Fudenberg & David Levine, 2008. "Limit Games and Limit Equilibria," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 2, pages 21-39, World Scientific Publishing Co. Pte. Ltd..
    2. Bruno Biais & Thomas Mariotti & Guillaume Plantin & Jean-Charles Rochet, 2007. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 345-390.
    3. 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..
    4. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    5. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2008. "Trees and extensive forms," Journal of Economic Theory, Elsevier, vol. 143(1), pages 216-250, November.
    6. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    7. repec:hal:wpaper:hal-02058235 is not listed on IDEAS
    8. Ehud Lehrer, 1992. "Correlated Equilibria in Two-Player Repeated Games with Nonobservable Actions," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 175-199, February.
    9. Drew Fudenberg & David K. Levine, 2009. "Repeated Games with Frequent Signals," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(1), pages 233-265.
    10. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    11. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    12. Cardaliaguet, Pierre & Rainer, Catherine & Rosenberg, Dinah & Vieille , Nicolas, 2013. "Markov Games with Frequent Actions and Incomplete Information," HEC Research Papers Series 1007, HEC Paris.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Staudigl, Mathias, 2016. "On Repeated games with imperfect public monitoring: Characterization of Continuation payoff processes," Center for Mathematical Economics Working Papers 526, Center for Mathematical Economics, Bielefeld University.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Sugaya, Takuo & Wolitzky, Alexander, 2017. "Bounding equilibrium payoffs in repeated games with private monitoring," Theoretical Economics, Econometric Society, vol. 12(2), May.
    3. Jérôme Renault & Tristan Tomala, 2011. "General Properties of Long-Run Supergames," Dynamic Games and Applications, Springer, vol. 1(2), pages 319-350, June.
    4. Ashkenazi-Golan, Galit & Lehrer, Ehud, 2019. "What you get is what you see: Cooperation in repeated games with observable payoffs," Journal of Economic Theory, Elsevier, vol. 181(C), pages 197-237.
    5. 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..
    6. 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.
    7. Urbano, A. & Vila, J. E., 2004. "Unmediated communication in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 46(1), pages 143-173, January.
    8. Sugaya, Takuo & Wolitzky, Alexander, 2018. "Bounding payoffs in repeated games with private monitoring: n-player games," Journal of Economic Theory, Elsevier, vol. 175(C), pages 58-87.
    9. Osório-Costa, António M., 2009. "Frequent Monitoring in Repeated Games under Brownian Uncertainty," MPRA Paper 13104, University Library of Munich, Germany.
    10. Olivier Gossner & Tristan Tomala, 2007. "Secret Correlation in Repeated Games with Imperfect Monitoring," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 413-424, May.
    11. Jan-Henrik Steg, 2018. "On Preemption in Discrete and Continuous Time," Dynamic Games and Applications, Springer, vol. 8(4), pages 918-938, December.
    12. Daehyun Kim & Ichiro Obara, 2023. "Asymptotic Value of Monitoring Structures in Stochastic Games," Papers 2308.09211, arXiv.org, revised Jul 2024.
    13. Tomala, Tristan, 2009. "Perfect communication equilibria in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 67(2), pages 682-694, November.
    14. Kuvalekar, Aditya & Lipnowski, Elliot & Ramos, João, 2022. "Goodwill in communication," Journal of Economic Theory, Elsevier, vol. 203(C).
    15. Osório-Costa, António M., 2009. "Efficiency Gains in Repeated Games at Random Moments in Time," MPRA Paper 13105, University Library of Munich, Germany.
    16. 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.
    17. Sugaya, Takuo & Yamamoto, Yuichi, 2020. "Common learning and cooperation in repeated games," Theoretical Economics, Econometric Society, vol. 15(3), July.
    18. Yutaka Kayaba & Hitoshi Matsushima & Tomohisa Toyama, 2016. "Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring:Experiments and Theory," CIRJE F-Series CIRJE-F-1004, CIRJE, Faculty of Economics, University of Tokyo.
    19. Kimmo Berg & Gijs Schoenmakers, 2017. "Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games," Games, MDPI, vol. 8(4), pages 1-14, November.
    20. , & ,, 2015. "A folk theorem for stochastic games with infrequent state changes," Theoretical Economics, Econometric Society, vol. 10(1), January.

    More about this item

    Keywords

    Continuous-time game theory; Stochastic optimal control; Weak convergence;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:525. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.