The existence of Nash equilibrium in n-person games with C-concavity

The purpose of this paper is to introduce the C-concavity condition, and next prove a new existence theorem of Nash equilibrium in n-person games with C-concavity. And, as an application, we shall prove a minimax theorem. Finally, we shall give some examples of a two-person game where the C-concavity can be applied, but the previous general concavity conditions cannot be applied. Our results generalize the corresponding results due to Nash and Forgö in several ways.