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Majorized correspondences and equilibrium existence in discontinuous games

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  • Pavlo Prokopovych

    (Kyiv School of Economics)

Abstract

This paper is aimed at widening the scope of applications of majorized correspondences. A new class of majorized correspondences—domain $${\mathcal {U}}$$ U -majorized correspondences—is introduced. For them, a maximal element existence theorem is established. Then, sufficient conditions for the existence of an equilibrium in qualitative games are provided. They are used to show the existence of a pure strategy Nash equilibrium in compact quasiconcave games that are either correspondence secure or correspondence transfer continuous.

Suggested Citation

  • Pavlo Prokopovych, 2016. "Majorized correspondences and equilibrium existence in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 541-552, March.
    • Handle: RePEc:spr:joecth:v:61:y:2016:i:3:d:10.1007_s00199-015-0874-y
    DOI: 10.1007/s00199-015-0874-y
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    Cited by:

    1. 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.
    2. 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.
    3. Vincenzo Scalzo, 2018. "Weak maximal elements and weak equilibria in ordinal games with applications to exchange economies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(1), pages 29-39, April.
    4. 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.
    5. Yang, Zhe & Yuan, George Xianzhi, 2019. "Some generalizations of Zhao’s theorem: Hybrid solutions and weak hybrid solutions for games with nonordered preferences," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 94-100.
    6. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    7. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.

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    More about this item

    Keywords

    Majorized correspondence; Qualitative game; Better-reply secure game; Correspondence secure game; Transfer continuous game;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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