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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
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    File URL: https://pub.uni-bielefeld.de/download/2698781/2902680
    File Function: First Version, 2014
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    References listed on IDEAS

    as
    1. Fabien Gensbittel, 2016. "Continuous-time limit of dynamic games with incomplete information and a more informed player," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 321-352, March.
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    3. Drew Fudenberg & David K. Levine, 2008. "Continuous time limits of repeated games with imperfect public monitoring," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 17, pages 369-388 World Scientific Publishing Co. Pte. Ltd..
    4. Drew Fudenberg & David K. Levine, 2009. "Repeated Games with Frequent Signals," The Quarterly Journal of Economics, Oxford University Press, vol. 124(1), pages 233-265.
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    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. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    8. Bruno Biais & Thomas Mariotti & Guillaume Plantin & Jean-Charles Rochet, 2007. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 345-390.
    9. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2008. "Trees and extensive forms," Journal of Economic Theory, Elsevier, vol. 143(1), pages 216-250, November.
    10. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273 World Scientific Publishing Co. Pte. Ltd..
    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.
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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. 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.

    More about this item

    Keywords

    Continuous-time game theory; Stochastic optimal control; Weak convergence;

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