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Games with Imperfectly Observable Actions in Continuous Time

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  • Yuliy Sannikov
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    Abstract

    This paper investigates a new class of two-player games in continuous time, in which the players' observations of each other's actions are distorted by Brownian motions. These games are analogous to repeated games with imperfect monitoring in which the players take actions frequently. Using a differential equation, we find the set ℰ(r) of payoff pairs achievable by all public perfect equilibria of the continuous-time game, where r is the discount rate. The same differential equation allows us to find public perfect equilibria that achieve any value pair on the boundary of the set ℰ(r). These public perfect equilibria are based on a pair of continuation values as a state variable, which moves along the boundary of ℰ(r) during the course of the game. In order to give players incentives to take actions that are not static best responses, the pair of continuation values is stochastically driven by the players' observations of each other's actions along the boundary of the set ℰ(r). Copyright The Econometric Society 2007.

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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2007.00795.x
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    Bibliographic Info

    Article provided by Econometric Society in its journal Econometrica.

    Volume (Year): 75 (2007)
    Issue (Month): 5 (09)
    Pages: 1285-1329

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    Handle: RePEc:ecm:emetrp:v:75:y:2007:i:5:p:1285-1329

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    Cited by:
    1. Kyna Fong, 2007. "Evaluating Skilled Experts: Optimal Scoring Rules for Surgeons," Discussion Papers 07-043, Stanford Institute for Economic Policy Research.
    2. Osório-Costa, António M., 2009. "Efficiency Gains in Repeated Games at Random Moments in Time," MPRA Paper 13105, University Library of Munich, Germany.
    3. Zhang, Yuzhe, 2009. "Dynamic contracting with persistent shocks," Journal of Economic Theory, Elsevier, vol. 144(2), pages 635-675, March.
    4. Osório Costa, Antonio Miguel, 2011. "Public Monitoring with Uncertainty in the Time Repetitions," Working Papers 2072/179668, Universitat Rovira i Virgili, Department of Economics.
    5. Tadashi Hashimoto, 2010. "Corrigendum to "Games With Imperfectly Observable Actions in Continuous Time"," Econometrica, Econometric Society, vol. 78(3), pages 1155-1159, 05.
    6. Wren-Lewis, Liam, 2013. "Commitment in utility regulation: A model of reputation and policy applications," Journal of Economic Behavior & Organization, Elsevier, vol. 89(C), pages 210-231.
    7. Takizawa, Shinichiro, 2010. "Private monitoring games and decisions under uncertainty," Economics Letters, Elsevier, vol. 108(3), pages 337-340, September.
    8. 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.
    9. Mason, Robin & Välimäki, Juuso, 2008. "Dynamic Moral Hazard and Project Completion," CEPR Discussion Papers 6857, C.E.P.R. Discussion Papers.
    10. 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.
    11. 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.
    12. Osório-Costa, António M., 2009. "Frequent Monitoring in Repeated Games under Brownian Uncertainty," MPRA Paper 13104, University Library of Munich, Germany.
    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. Chandrasekher, Madhav, 0. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society.
    15. Kobayashi, Hajime & Ohta, Katsunori, 2008. "Multimarket contact in continuous-time games," Economics Letters, Elsevier, vol. 101(1), pages 4-5, October.

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