On the existence of Nash equilibrium in discontinuous games

Rabia Nessah (1) , Guoqiang Tian

1 LEM - Lille économie management - UMR 9221

This paper offers an equilibrium existence theorem in discontinuous games. We introduce a new notion of very weak continuity, called quasi-weak transfer continuity that guarantees the existence of pure strategy Nash equilibrium in compact and quasiconcave games. We also consider possible extensions and improvements of the main result. We present applications to show that our conditions allow for economically meaningful payoff discontinuities.

Mots clés: Discontinuous games; Quasi-weak transfer continuity; Various notions of transfer continuity; Nash equilibrium

Domaines: Economies et finances

Rabia Nessah, Guoqiang Tian. On the existence of Nash equilibrium in discontinuous games. Economic Theory, 2015, 61 (3), pp.515--540. ⟨10.1007/s00199-015-0921-8⟩. ⟨hal-01533554⟩