A note on the existence of Berge and Berge-Nash equilibria

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 3.2–3.3 [Abalo, K.Y., Kostreva, M.M., 1996. Fixed Points, Nash Games and their Organization. Topological Methods in Nonlinear Analysis 8, 205–215.]. In this paper we show that the assumptions of these theorems are actually not sufficient for the existence of Berge equilibrium. We then propose a new version of these theorems. © 2007 Elsevier B.V. All rights reserved.