Nash Equilibria for Noncooperative n-Person Games in Normal Form

Abstract

This paper concentrates on the problem of the existence of $\varepsilon $-equilibrium points in the Nash sense for noncooperative n-person games in normal form. Firstly, a survey of known $\varepsilon $-equilibrium.point theorems and proof techniques is given. Then various new $\varepsilon $-equilibrium point theorems are derived, in which one of the players has a big strategy space and where nonbounded, payoff functions are allowed. To prove these theorems, results of Arzela–Ascoli are extended.