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...

Embarking from the concept of uniform payoff security (Monteiro P.K., Page F.H, J Econ Theory 134: 566-575, 2007), we introduce two other uniform conditions and then study the existence of mixed strategy Nash equilibria in games where the sum of the payoff functions is not necessarily upper...

A short proof of Reny (1999)'s equilibrium existence theorem for payoff secure games is provided. At the heart of the proof lies the concept of a multivalued mapping with the local intersection property. By means of the Fan-Browder collective fixed-point theorem, we show an approximate...