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

Bertrand Crettez, Rabia Nessah () and Tarik Tazdaït ()
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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

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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].

Keywords: better-reply correspondence.; discontinuous game; Nash equilibrium (search for similar items in EconPapers)
Date: 2025-07-31
New Economics Papers: this item is included in nep-inv and nep-mic
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Published in International Game Theory Review, 2025, 27 (03), ⟨10.1142/S0219198925500070⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05305754

DOI: 10.1142/S0219198925500070

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