  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.
