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Feasibility and individual rationality in two-person Bayesian games

Author

Listed:
  • Francoise Forges

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, LEDa - Laboratoire d'Economie de Dauphine - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres)

  • Ulrich Horst

    (Institut für Mathematik [Berlin] - TUB - Technical University of Berlin / Technische Universität Berlin, HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin, Department of Mathematics - HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin)

  • Antoine Salomon

    (LEDa - Laboratoire d'Economie de Dauphine - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres)

Abstract

We define feasible, posterior individually rational solutions for two-person Bayesian games with a single informed player. Such a solution can be achieved by direct signalling from the informed player and requires approval of both players after the signal has been sent. Without further assumptions on the Bayesian game, a solution does not necessarily exist. We show that, if the uninformed player has a "uniform punishment strategy" against the informed one, the existence of a solution follows from the existence of Nash equilibrium in infinitely repeated games with lack of information on one side. We also consider the extension of the result when both players have private information.

Suggested Citation

  • Francoise Forges & Ulrich Horst & Antoine Salomon, 2016. "Feasibility and individual rationality in two-person Bayesian games," Post-Print hal-02276751, HAL.
    • Handle: RePEc:hal:journl:hal-02276751
    DOI: 10.1007/s00182-015-0520-8
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    Cited by:

    1. Forges, Françoise & Horst, Ulrich, 2018. "Sender–receiver games with cooperation," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 52-61.
    2. Raghul S Venkatesh, 2018. "Communication and Commitment with Constraints," AMSE Working Papers 1856, Aix-Marseille School of Economics, France, revised Jul 2019.
    3. Lucas Pahl, 2021. "Information Spillover in Multiple Zero-sum Games," Papers 2111.01647, arXiv.org, revised Mar 2023.
    4. Lucas Pahl, 2024. "Information spillover in multiple zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(1), pages 71-104, March.
    5. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.

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