A new proof for the existence of Nash equilibrium

TL;DR

This paper introduces a novel proof for the existence of Nash equilibrium that does not rely on fixed point theorems, providing a self-contained and alternative approach to a fundamental concept in game theory.

Contribution

The paper presents a new proof method for Nash equilibrium existence that avoids fixed point theorems, expanding theoretical understanding.

Findings

Existence of pre-equilibria established

Existence of Nash equilibria demonstrated

Proof is self-contained and does not use fixed point theorems

Abstract

We present a new proof for the existence of a Nash equilibrium, which involves no fixed point theorem. The self-contained proof consists of two parts. The first part introduces the notions of root function and pre-equilibrium. The second part shows the existence of pre-equilibria and Nash equilibria.