Generalized weak transfer continuity and the Nash equilibrium

Abstract

This paper introduces the notion of generalized weak transfer continuity and establishes that a bounded, compact locally convex metric quasiconcave and generalized weak transfer continuous game has a Nash equilibrium. Our equilibrium existence result neither implies nor is implied by the existing results in the literature such as those in [Carmona, G., 2011. Understanding some recent existence results for discontinuous games. Economic Theory 48, 31–45], [Prokopovych, P., 2011. On equilibrium existence in payoff secure games. Economic Theory 48, 5–16], [Carmona, G., 2009. An existence result for discontinuous games. Journal of Economic Theory 144, 1333–1340], and [Reny, P.J., 1999. On the existence of pure and mixed strategy Nash equilibria in discontinuous games, Econometrica 67, 1029–1056].