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On the existence of Nash equilibrium in Bayesian games

Author

Listed:
  • Oriol Carbonell-Nicolau

    (Rutgers University)

  • Richard McLean

    (Rutgers University)

Abstract

We furnish conditions on the primitives of a Bayesian game that guarantee the existence of a Bayes-Nash equilibrium. We consider spaces of distributional and behavioral strategies, and highlight the relationship between their respective topologies, which implies that the two spaces are mutually interchangeable throughout the analysis. By allowing for payoff discontinuities in actions, we cover various applications that cannot be handled by extant results.

Suggested Citation

  • Oriol Carbonell-Nicolau & Richard McLean, 2014. "On the existence of Nash equilibrium in Bayesian games," Departmental Working Papers 201402, Rutgers University, Department of Economics.
    • Handle: RePEc:rut:rutres:201402
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    Cited by:

    1. Bich, Philippe & Laraki, Rida, 2017. "On the existence of approximate equilibria and sharing rule solutions in discontinuous games," Theoretical Economics, Econometric Society, vol. 12(1), January.
    2. Oriol Carbonell-Nicolau, 2015. "Semicontinuous integrands as jointly measurable maps," Departmental Working Papers 201512, Rutgers University, Department of Economics.
    3. Oriol Carbonell-Nicolau, 2021. "Equilibria in infinite games of incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 311-360, June.
    4. Kos, Nenad & Auster, Sarah & Piccolo, Salvatore, 2019. "Optimal Selling Mechanisms with Endogenous Proposal Rights," CEPR Discussion Papers 13542, C.E.P.R. Discussion Papers.
    5. He, Wei & Yannelis, Nicholas C., 2015. "Discontinuous games with asymmetric information: An extension of Reny's existence theorem," Games and Economic Behavior, Elsevier, vol. 91(C), pages 26-35.
    6. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    7. Philip Brookins & Dmitry Ryvkin, 2016. "Equilibrium existence in group contests," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 265-276, October.
    8. Wei He & Nicholas C. Yannelis, 2017. "A remark on discontinuous games with asymmetric information and ambiguity," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 119-126, April.
    9. Oriol Carbonell-Nicolau, 2021. "Perfect equilibria in games of incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1591-1648, June.

    More about this item

    Keywords

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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