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Repeated games with public deterministic monitoring

Author

Listed:
  • Marie Laclau

    (PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Tristan Tomala

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider repeated games with compact actions sets and pure strategies in which players commonly observe a public signal which reveals imperfectly the action profile. We characterize the set of payoffs profiles that can be sustained by a perfect equilibrium, as players become increasingly patient. There are two conditions: admissibility and joint rationality. An admissibly feasible payoff can be achieved by an action profile that offers no unilateral deviation which is both undetectable and profitable. It is jointly rational if for all weights on players, the weighted average payoff is greater than or equal to the minmax level of the weighted average payoff function. This characterization is alternative to the one provided by the "score method" of Fudenberg and Levine (1994). We provide a simple construction of equilibrium strategies based on cooperation, punishments and rewards. Punishments rely on Blackwell's approachability algorithm.

Suggested Citation

  • Marie Laclau & Tristan Tomala, 2017. "Repeated games with public deterministic monitoring," PSE-Ecole d'économie de Paris (Postprint) halshs-01503768, HAL.
    • Handle: RePEc:hal:pseptp:halshs-01503768
    DOI: 10.1016/j.jet.2017.02.011
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    References listed on IDEAS

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    1. Tristan Tomala, 1998. "Pure equilibria of repeated games with public observation," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 93-109.
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    Cited by:

    1. Simo Sun & Hui Yang & Guanghui Yang & Jinxiu Pi, 2021. "Evolutionary Games and Dynamics in Public Goods Supply with Repetitive Actions," Mathematics, MDPI, vol. 9(15), pages 1-16, July.

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    More about this item

    Keywords

    Repeated games; Public monitoring; Pure strategies; Approachability;
    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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