This paper characterizes the existence of equilibria in minimax inequalities without assuming any form of quasiconcavity of functions and convexity or compactness of choice sets. A new condition, called " local dominatedness property " , is shown to be necessary and further, under some mild continuity condition, sufficient for the existence of equilibrium.… (More)
This paper investigates the existence of strong Nash equilibria (SNE) in continuous and concave games. We show that the coalition consistence property introduced in the paper, together with the concavity and continuity of payoffs, permits the existence of strong Nash equilibria in games with compact and convex strategy spaces. The coalition consistency… (More)
This paper deals with the problem of existence of Berge and Berge–Nash equilibria. Abalo and Kostreva have proved existence theorems of Berge and Berge–Nash equilibria for S-equi-well-posed and (S, σ)-equi-well-posed games, namely, Theorems 3. In this paper we show that the assumptions of these theorems are actually not sufficient for the existence of Berge… (More)
This paper investigates the existence of pure strategy, dominant strategy, and mixed strategy Nash equilibria in discontinuous and/or nonconvex games. We introduce a new notion of very weak continuity, called weak transfer quasi-continuity, which is weaker than the most known weak notions of continuity, including diagonal transfer continuity in Baye et al.… (More)
In this paper, we study the main properties of the strong Berge equilibrium which is also a Pareto efficient (SBPE) and the strong Nash equilibrium (SNE). We prove that any SBPE is also a SNE, we prove also existence theorem of SBPE based on the Ky Fan inequality. Finally, we also provide a method for computing SPBE.