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Nash Equilibrium in Discontinuous Games: A Weakening of Reny’s Robust Better-Reply Correspondence Property

Author

Listed:
  • Bertrand Crettez

    (Université Paris-Panthéon-Assas, LEMMA)

  • Rabia Nessah

    (IESEG School of Management, UMR 9221 – LEM – Lille Economie Management, F-59000 Lille, France)

  • Tarik Tazdaït

    (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 - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris)

Abstract

This paper weakens the notion of robust better-reply correspondence property introduced in [Reny, P. J. [2020] Nash equilibrium in discontinuous games, Annu. Rev. Econ. 12, 439–470] to prove the existence of pure strategy Nash equilibrium in compact convex discontinuous and possibly nonquasiconcave games. Our weakening of this property is satisfied by a large class of these games and our equilibrium existence results strictly generalize the most important ones in the literature, namely those obtained in [Reny, P. J. [2020] Nash equilibrium in discontinuous games, Annu. Rev. Econ. 12, 439–470; Reny, P. [2016b] Introduction to the symposium on discontinuous games, Econ. Theory 61, 423–429; Carmona, G. and Podczeck, K. [2016] Existence of Nash equilibrium in ordinal games with discontinuous preferences, Econ. Theory 61, 457–478] (in a special case), [Reny, P. [1999] On the existence of pure and mixed strategy Nash equilibria in discontinuous games, Econometrica 67, 1029–1056; McLennan, A., Monteiro, P. K. and Tourky, R. [2011] Games with discontinuous payoffs: A strengthening of Reny's existence theorem, Econometrica 79, 1643–1664; Barelli, P. and Meneghel, I. [2013] A note on the equilibrium existence problem in discontinuous games, Econometrica 81, 813–824; Nessah, R. [2011] Generalized weak transfer continuity and Nash equilibrium, J. Math. Econ. 47, 659–662; Nessah, R. and Tian, G. [2016] On the existence of Nash equilibrium in discontinuous games, Econ. Theory 61, 515–540].

Suggested Citation

  • Bertrand Crettez & Rabia Nessah & Tarik Tazdaït, 2025. "Nash Equilibrium in Discontinuous Games: A Weakening of Reny’s Robust Better-Reply Correspondence Property," Post-Print hal-05305754, HAL.
    • Handle: RePEc:hal:journl:hal-05305754
    DOI: 10.1142/S0219198925500070
    Note: View the original document on HAL open archive server: https://hal.science/hal-05305754v1
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    References listed on IDEAS

    as
    1. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, March.
    2. Philip J. Reny, 2016. "Introduction to the symposium on discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 423-429, March.
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