Some Algebraic Properties of a Subclass of Finite Normal Form Games

TL;DR

This paper introduces algebraic methods for computing all Nash equilibria in a specific subclass of finite normal form games and provides a way to determine if a game belongs to this class.

Contribution

It offers a novel algebraic characterization and computational approach for Nash equilibria in a particular subclass of finite normal form games.

Findings

Method successfully computes all Nash equilibria for the subclass.

Decides membership to the subclass with related algebraic criteria.

Includes an illustrative example demonstrating the methods.

Abstract

We study the problem of computing all Nash equilibria of a subclass of finite normal form games. With algebraic characterization of the games, we present a method for computing all its Nash equilibria. Further, we present a method for deciding membership to the class of games with its related results. An appendix, containing an example to show working of each of the presented methods, concludes the work.