Constructive proof of the existence of Nash equilibrium in a strategic game with sequentially locally non-constant payoff functions

Abstract

In this paper we constructively prove the existence of Nash equilibrium in a finite strategic game with sequentially locally non-constant payoff functions by a constructive version of Kakutani's fixed point theorem for sequentially locally non-constant multi-functions (multi-valued functions or correspondences). We also examine the existence of Nash equilibrium in a game with continuous strategies and quasi-concave payoff functions which has sequentially locally at most one maximum. We follow the Bishop style constructive mathematics.