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Pure-strategy equilibrium in Bayesian potential games with absolutely continuous information

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  • Einy, Ezra
  • Haimanko, Ori

Abstract

We prove the existence of a pure-strategy Bayesian Nash equilibrium in Bayesian games with absolutely continuous information and a Bayesian potential that is upper semi-continuous in actions for any realization of the players' types. In particular, all Bayesian potential games with finitely many actions and absolutely continuous information possess a pure-strategy Bayesian Nash equilibrium.

Suggested Citation

  • Einy, Ezra & Haimanko, Ori, 2023. "Pure-strategy equilibrium in Bayesian potential games with absolutely continuous information," Games and Economic Behavior, Elsevier, vol. 140(C), pages 341-347.
    • Handle: RePEc:eee:gamebe:v:140:y:2023:i:c:p:341-347
    DOI: 10.1016/j.geb.2023.04.004
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    References listed on IDEAS

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    1. He, Wei & Sun, Yeneng, 2019. "Pure-strategy equilibria in Bayesian games," Journal of Economic Theory, Elsevier, vol. 180(C), pages 11-49.
    2. Philip J. Reny, 2011. "On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games," Econometrica, Econometric Society, vol. 79(2), pages 499-553, March.
    3. Van Zandt, Timothy & Vives, Xavier, 2007. "Monotone equilibria in Bayesian games of strategic complementarities," Journal of Economic Theory, Elsevier, vol. 134(1), pages 339-360, May.
    4. Oriol Carbonell-Nicolau & Richard P. McLean, 2018. "On the Existence of Nash Equilibrium in Bayesian Games," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 100-129, February.
    5. M. Khan & Kali Rath & Yeneng Sun, 2006. "The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 91-104, April.
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    7. Einy, Ezra & Haimanko, Ori, 2020. "Equilibrium existence in games with a concave Bayesian potential," Games and Economic Behavior, Elsevier, vol. 123(C), pages 288-294.
    8. Raith, Michael, 1996. "A General Model of Information Sharing in Oligopoly," Journal of Economic Theory, Elsevier, vol. 71(1), pages 260-288, October.
    9. Balder, Erik J & Yannelis, Nicholas C, 1993. "On the Continuity of Expected Utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(4), pages 625-643, October.
    10. Takashi Ui, 2009. "Bayesian potentials and information structures: Team decision problems revisited," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(3), pages 271-291, September.
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    More about this item

    Keywords

    Bayesian games; Bayesian potential; Pure-strategy equilibrium; Continuous payoffs; Absolute continuity of information; Purification;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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