Kakutani's fixed point theorem for multi-functions with sequentially at most one fixed point and the minimax theorem for two-person zero-sum games: A constructive analysis

Abstract

In this paper we constructively prove Kakutani's fixed point theorem for multi-functions with sequentially at most one fixed point and uniformly closed graph, and apply this result to prove the minimax theorem for two-person zero-sum games with finite strategies. We follow the Bishop style constructive mathematics.