A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games

Several relaxations of Nash equilibrium are shown to exist in strategic games with discontinuous payoff functions. Those relaxations are used to extend and unify several recent results and link Reny’s better-reply security condition [Reny, P.J. (1999). On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games. Econometrica, 67(5), 1029-1056.] to Simon-Zame’s endogenous tie-breaking rules [Simon, L.K. and Zame, W.R. (1990). Discontinuous Games and Endogenous Sharing Rules. Econometrica, 58, 861-872.].