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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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    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. Fudenberg, Drew & Ishii, Yuhta & Kominers, Scott Duke, 2014. "Delayed-response strategies in repeated games with observation lags," Scholarly Articles 11880354, Harvard University Department of Economics.
    2. Osório Costa, Antonio Miguel, 2011. "A Folk Theorem for Games when Frequent Monitoring Decreases Noise," Working Papers 2072/179667, Universitat Rovira i Virgili, Department of Economics.
    3. Zhang, Yuzhe, 2009. "Dynamic Contracting with Persistent Shocks," MPRA Paper 23108, University Library of Munich, Germany.
    4. Mason, Robin & Välimäki, Juuso, 2008. "Dynamic Moral Hazard and Project Completion," CEPR Discussion Papers 6857, C.E.P.R. Discussion Papers.
    5. Kyna Fong, 2007. "Evaluating Skilled Experts: Optimal Scoring Rules for Surgeons," Discussion Papers 07-043, Stanford Institute for Economic Policy Research.
    6. Kobayashi, Hajime & Ohta, Katsunori, 2008. "Multimarket contact in continuous-time games," Economics Letters, Elsevier, vol. 101(1), pages 4-5, October.
    7. Wälde, Klaus & Bayer, Christian, 2011. "Describing the Dynamics of Distribution in Search and Matching Models by Fokker-Planck Equations," Annual Conference 2011 (Frankfurt, Main): The Order of the World Economy - Lessons from the Crisis 48736, Verein für Socialpolitik / German Economic Association.
    8. Drew Fudenberg & David K Levine, 2013. "Tail Probabilities for Triangular Arrays," Levine's Working Paper Archive 786969000000000685, David K. Levine.
    9. 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.
    10. Hashimoto, Tadashi, 2007. "A corrigendum to "Games with imperfectly observable actions in continuous time"," MPRA Paper 5398, University Library of Munich, Germany.
    11. Osório-Costa, António M., 2009. "Efficiency Gains in Repeated Games at Random Moments in Time," MPRA Paper 13105, University Library of Munich, Germany.
    12. Chandrasekher, Madhav, 0. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society.
    13. Osório Costa, Antonio Miguel, 2011. "Public Monitoring with Uncertainty in the Time Repetitions," Working Papers 2072/179668, Universitat Rovira i Virgili, Department of Economics.
    14. Takizawa, Shinichiro, 2010. "Private monitoring games and decisions under uncertainty," Economics Letters, Elsevier, vol. 108(3), pages 337-340, September.
    15. 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.
    16. Osório-Costa, António M., 2009. "Frequent Monitoring in Repeated Games under Brownian Uncertainty," MPRA Paper 13104, University Library of Munich, Germany.

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