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Reputation Effects and Equilibrium Degeneracy in Continuous-Time Games

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Abstract

We study a class of continuous-time reputation games between a large player and a population of small players in which the actions of the large player are imperfectly observable. The large player is either a normal type, who behaves strategically, or a behavioral type, who is committed to playing a certain strategy. We provide a complete characterization of the set of sequential equilibrium payoffs of the large player using an ordinary differential equation. In addition, we identify a sufficient condition for the sequential equilibrium to be unique and Markovian in the small players' posterior belief. An implication of our characterization is that when the small players are certain that they are facing the normal type, intertemporal incentives are trivial: the set of equilibrium payoffs of the large player coincides with the convex hull of the set of static Nash equilibrium payoffs.

Suggested Citation

  • Eduardo Faingold & Yuliy Sannikov, 2007. "Reputation Effects and Equilibrium Degeneracy in Continuous-Time Games," Cowles Foundation Discussion Papers 1624, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1624
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d16/d1624.pdf
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    1. Eduardo Faingold & Yuliy Sannikov, 2007. "Equilibrium Degeneracy and Reputation Effects," NajEcon Working Paper Reviews 843644000000000216, www.najecon.org.
    2. Eduardo Faingold & Yuri Sannikov, 2007. "Reputation Effects and Equilibrium Degeneracy in Continuous Time Games," Levine's Bibliography 122247000000001487, UCLA Department of Economics.
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    Cited by:

    1. Li, Jingyuan & Liu, Yongming & Tian, Guoqiang, 2009. "A reputation strategic model of monetary policy in continuous-time," Journal of Macroeconomics, Elsevier, vol. 31(4), pages 523-533, December.
    2. Kyna Fong, "undated". "Evaluating Skilled Experts: Optimal Scoring Rules for Surgeons," Discussion Papers 07-043, Stanford Institute for Economic Policy Research.
    3. Eduardo Faingold & Yuri Sannikov, 2007. "Reputation Effects and Equilibrium Degeneracy in Continuous Time Games," Levine's Bibliography 122247000000001487, UCLA Department of Economics.
    4. 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.
    5. Osório-Costa, António M., 2009. "Frequent Monitoring in Repeated Games under Brownian Uncertainty," MPRA Paper 13104, University Library of Munich, Germany.
    6. Osório-Costa, António M., 2009. "Efficiency Gains in Repeated Games at Random Moments in Time," MPRA Paper 13105, University Library of Munich, Germany.

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    More about this item

    Keywords

    Repeated games; Reputation; Continuous time;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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