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High frequency repeated games with costly monitoring

Author

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  • Lehrer, Ehud

    (Tel Aviv University, INSEAD)

  • Solan, Eilon

    (School of Mathematical Sciences, Tel Aviv University)

Abstract

We study two-player discounted repeated games in which a player cannot monitor the other unless he pays a fixed amount. It is well known that in such a model the folk theorem holds when the monitoring cost is of the order of magnitude of the stage payoff. We analyze high frequency games in which the monitoring cost is small but still significantly higher than the stage payoff. We characterize the limit set of public perfect equilibrium payoffs as the monitoring cost tends to 0. It turns out that this set is typically a strict subset of the set of feasible and individually rational payoffs. In particular, there might be efficient and individually rational payoffs that cannot be sustained in equilibrium. We also make an interesting connection between games with costly monitoring and games played between long-lived and short-lived players. Finally, we show that the limit set of public perfect equilibrium payoffs coincides with the limit set of Nash equilibrium payoffs. This implies that our characterization applies also to sequential equilibria.

Suggested Citation

  • Lehrer, Ehud & Solan, Eilon, 2018. "High frequency repeated games with costly monitoring," Theoretical Economics, Econometric Society, vol. 13(1), January.
  • Handle: RePEc:the:publsh:2627
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    References listed on IDEAS

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    Cited by:

    1. Hino, Yoshifumi, 2019. "An efficiency result in a repeated prisoner’s dilemma game under costly observation with nonpublic randomization," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 47-53.

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    More about this item

    Keywords

    High frequency repeated games; costly monitoring; Nash equilibrium; public perfect equilibrium; no folk theorem; characterization;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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