Neumann-Morgenstern Stable Set of a Finite Static Game

In order to solve the difficulty that players want to realize a pure Nash equilibria in a static finite game where principle of maximum entropy is all the players common knowledge, we introduce the concept of Neumann-Morgenstern stable set (briefly, N-M stable set) which is a subset of set of all pure Nash equilibria, give an algorithm to find N-M stable set, outline existence and uniqueness of N-M stable set in a finite static strategy game with at least one pure Nash equilibrium, and show that every finite static strategy game is equivalent to one and only one ideal game. Basic on those results, players are more intelligent and it is easier for they to want to realize a pure Nash equilibrium.