Brouwer's fixed point theorem with sequentially at most one fixed point

TL;DR

This paper provides a constructive proof of Brouwer's fixed point theorem ensuring at most one fixed point, and demonstrates its application to the mini-max theorem in zero-sum games.

Contribution

It introduces a constructive proof of Brouwer's fixed point theorem with a unique fixed point condition and applies it to game theory.

Findings

Constructive proof of Brouwer's fixed point theorem

Application to mini-max theorem in zero-sum games

Establishment of at most one fixed point in the proof

Abstract

We present a constructive proof of Brouwer's fixed point theorem with sequentially at most one fixed point, and apply it to the mini-max theorem of zero-sum games.