An Algebraic Approach for Computing Equilibria of a Subclass of Finite Normal Form Games

TL;DR

This paper introduces an algebraic method leveraging Galois groups to compute all Nash equilibria in a specific subclass of finite normal form games with rational payoffs and irrational equilibria.

Contribution

It presents a novel algebraic approach using Galois theory to efficiently find all Nash equilibria in a new class of games.

Findings

The method successfully computes all equilibria for the defined game class.

Properties of the game subclass are characterized.

An illustrative example demonstrates the method's application.

Abstract

A Nash equilibrium has become important solution concept for analyzing the decision making in Game theory. In this paper, we consider the problem of computing Nash equilibria of a subclass of generic finite normal form games. We define "rational payoff irrational equilibria games" to be the games with all rational payoffs and all irrational equilibria. We present a purely algebraic method for computing all Nash equilibria of these games that uses knowledge of Galois groups. Some results, showing properties of the class of games, and an example to show working of the method concludes the paper.