Some Algebraic Properties of a Subclass of Finite Normal Form Games

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.