Applications of Algebra for Some Game Theoretic Problems

摘要

In this paper we present applications of polynomial algebra for the problem of computing Nash equilibria of a subclass of finite normal form games. We characterize Nash equilibria of a normal form game as solutions to a system of polynomial equations and define the subclass of games under consideration. We present an algebraic method for deciding membership decision to the subclass of games. A method based on group action to compute all Nash equilibria of the subclass of games is presented with examples to show working of the methods. We also present some related results and discuss properties of the subclass of games.