Nash equilibrium and minimax theorem with C-concavity

The purpose of this paper is to introduce a generalized C-concave condition, and by using Himmelberg’s fixed point theorem, to prove a new existence theorem of Nash equilibrium in non-compact generalized game with C-concavity. As applications, we shall prove a minimax theorem in non-compact settings and prove a minimax inequality in compact settings. © 2006 Elsevier Inc. All rights reserved.