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Nash and Bayes–Nash equilibria in strategic-form games with intransitivities

Author

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  • Oriol Carbonell-Nicolau

    (Rutgers University)

  • Richard P. McLean

    (Rutgers University)

Abstract

We study games with intransitive preferences that admit skew-symmetric representations. We introduce the notion of surrogate better-reply security for discontinuous skew-symmetric games and elucidate the relationship between surrogate better-reply security and other security concepts in the literature. We then prove existence of behavioral strategy equilibrium for discontinuous skew-symmetric games of incomplete information (and, in particular, existence of mixed-strategy equilibrium for discontinuous skew-symmetric games of complete information), generalizing extant results.

Suggested Citation

  • Oriol Carbonell-Nicolau & Richard P. McLean, 2019. "Nash and Bayes–Nash equilibria in strategic-form games with intransitivities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 935-965, November.
    • Handle: RePEc:spr:joecth:v:68:y:2019:i:4:d:10.1007_s00199-018-1151-7
    DOI: 10.1007/s00199-018-1151-7
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    Cited by:

    1. 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.
    2. 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.
    3. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.

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    More about this item

    Keywords

    Skew-symmetric game; Bayesian game; Existence of Nash equilibrium; Discontinuous game; Behavioral strategy;
    All these keywords.

    JEL classification:

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

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