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Quasi-Transfer Continuity and Nash Equilibrium
[Continuité de quasi-transfert et équilibre de Nash]

Author

Listed:
  • Rabia Nessah
  • Tarik Tazdait

    (CIRED - centre international de recherche sur l'environnement et le développement - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - EHESS - École des hautes études en sciences sociales - AgroParisTech - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, EHESS - École des hautes études en sciences sociales, ENPC - École des Ponts ParisTech)

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 [G. Carmona, An existence result for discontinuous games, Journal of Economic Theory 144 (2009) 1333-1340]. We also show that our result is neither implied by nor does it imply the existence theorems of Reny [J.P. Reny, On the existence of pure and mixed strategy Nash equilibria in discontinuous games, Econometrica 67 (1999) 1029-1056] and Baye, Tian, and Zhou [M.R. Baye, G. Tian, J. Zhou, Characterizations of the existence of equilibria in games with discontinuous and non-quasiconcave payoffs, The Review of Economic Studies 60 (1993) 935-948].

Suggested Citation

  • Rabia Nessah & Tarik Tazdait, 2019. "Quasi-Transfer Continuity and Nash Equilibrium [Continuité de quasi-transfert et équilibre de Nash]," Post-Print hal-03592758, HAL.
    • Handle: RePEc:hal:journl:hal-03592758
    DOI: 10.1142/S021919891950004X
    Note: View the original document on HAL open archive server: https://hal.science/hal-03592758
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    References listed on IDEAS

    as
    1. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1333-1340, May.
    2. 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.
    3. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    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.
    Full references (including those not matched with items on IDEAS)

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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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