Constructive proof of the existence of Nash Equilibrium in a finite strategic game with sequentially locally non-constant payoff functions by Sperner's lemma

TL;DR

This paper provides a constructive proof of the existence of Nash equilibrium in finite strategic games with sequentially locally non-constant payoffs, utilizing Sperner's lemma within Bishop-style constructive mathematics.

Contribution

It introduces a new constructive proof method for Nash equilibrium existence using Sperner's lemma and Bishop-style mathematics.

Findings

Constructive proof of Nash equilibrium existence for specific payoff functions

Application of Sperner's lemma to game theory

Advancement in constructive mathematics approaches to game theory

Abstract

Using Sperner's lemma for modified partition of a simplex we will constructively prove the existence of a Nash equilibrium in a finite strategic game with sequentially locally non-constant payoff functions. We follow the Bishop style constructive mathematics.