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Quasi-Transfer Continuity and Nash Equilibrium

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. Theory144, 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, Econometrica67, 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. Studies60, 935–948].
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Submitted on : Tuesday, November 3, 2020 - 3:50:39 PM
Last modification on : Wednesday, November 3, 2021 - 4:17:25 AM

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Rabia Nessah, Tarik Tazdait. Quasi-Transfer Continuity and Nash Equilibrium. International Game Theory Review, World Scientific Publishing, 2019, 21 (4), pp.1950004. ⟨10.1142/S021919891950004X⟩. ⟨hal-02987150⟩

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