Quasi-Transfer Continuity and Nash Equilibrium

Rabia Nessah () and Tarik Tazdaït
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Rabia Nessah: IESEG School of Management, LEM-CNRS (UMR 9221), 3 rue de la Digue 59000 Lille, France

International Game Theory Review (IGTR), 2019, vol. 21, issue 04, 1-8

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].

Keywords: Nash equilibrium; discontinuity; quasi-transfer continuity (search for similar items in EconPapers)
JEL-codes: C70 C72 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S021919891950004X

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