On the Existence of Mixed Strategy Nash Equilibria

Abstract

The focus of this paper is on developing geometric sufficient conditions for the existence of a mixed strategy Nash equilibrium for both diagonally transfer continuous and better-reply secure games. First, we show that employing the concept of diagonal transfer continuity in place of better-reply security might be advantageous when the existence of a mixed strategy Nash equilibrium is concerned. Then, we study equilibrium existence in better-reply secure games possessing a payoff secure mixed extension. With the aid of an example we show that such games need not have mixed strategy Nash equilibria. We provide some easily verifiable conditions for the mixed extension of a two-person game that is reciprocally upper semicontinuous and uniformly payoff secure to be better-reply secure.

Keywords: Discontinuous game; Diagonally transfer continuous game; Better-reply secure game; Mixed strategy equilibrium; Transfer lower semicontinuity

JEL Classification: C65; C72