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Quasi-Transfer Continuity and Nash Equilibrium

Author

Listed:
  • Rabia Nessah

    (IESEG School of Management, LEM-CNRS (UMR 9221), 3 rue de la Digue 59000 Lille, France)

  • Tarik Tazdait

    (CIRED - CNRS - EHESS - Ecole des Ponts, Paristech, Campus du Jardin d’Agronomie Tropicale, 45 bis avenue de la Belle Gabrielle, 94736 Nogent sur Marne Cedex, France)

Abstract

We introduce a new notion of continuity, called quasi-transfer continuity, and show that it is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. This holds true in a large class of discontinuous games. We show that our result strictly generalizes the pure strategy existence theorem of Carmona [Carmona, G. [2009] An existence result for discontinuous games, J. Econ. Theory 144, 1333–1340]. We also show that our result is neither implied by nor does it imply the existence theorems of Reny [Reny, J. P. [1999] On the existence of pure and mixed strategy Nash equilibria in discontinuous games, Econometrica 67, 1029–1056] and Baye et al. [Baye, M. R., Tian, G. and Zhou, J. [1993] Characterizations of the existence of equilibria in games with discontinuous and nonquasiconcave payoffs, Rev. Econ. Studies 60, 935–948].

Suggested Citation

  • Rabia Nessah & Tarik Tazdait, 2019. "Quasi-Transfer Continuity and Nash Equilibrium," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-8, December.
  • Handle: RePEc:wsi:igtrxx:v:21:y:2019:i:04:n:s021919891950004x
    DOI: 10.1142/S021919891950004X
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    References listed on IDEAS

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    1. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1333-1340, May.
    2. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 935-948.
    3. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    4. Adib Bagh & Alejandro Jofre, 2006. "Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment," Econometrica, Econometric Society, vol. 74(6), pages 1715-1721, November.
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    More about this item

    Keywords

    Nash equilibrium; discontinuity; quasi-transfer continuity;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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