Quasi-Transfer Continuity and Nash Equilibrium *

Continuité de quasi-transfert et équilibre de Nash

Rabia Nessah , Tarik Tazdait (1, 2, 3)

1 CIRED - centre international de recherche sur l'environnement et le développement
2 EHESS - École des hautes études en sciences sociales
3 ENPC - École des Ponts ParisTech

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].

Mots clés: Nash equilibrium; discontinuity; quasi-transfer continuity

Domaines: Economies et finances

Rabia Nessah, Tarik Tazdait. Quasi-Transfer Continuity and Nash Equilibrium *. International Game Theory Review, 2019, ⟨10.1142/S021919891950004X⟩. ⟨hal-03592758⟩