Nash, Balanced And Refined In-depth Study

In this paper we study the refining of Nash equilibrium in game theory from the refining of the solution to the variational inequality. The main idea is to perturb simultaneously both the domain set X and the lolution concept. We get the concept of stable stationary. Then we use the new concept applied to the N-person noncooperative games theory to study the relation of proper equilibria and robust equilibria.In the chapter one and the chapter two, the development of game theory and the model of N-person noncooperative games and the definition of Nash equilibria are introduced. At the same time, the definition of perfect stationary, proper stationary and robust stationary of the variational inequality are given.In the chapter three we use the refining of variational inequality to the N-person noncooperative games.Chapter four gives some question which has not been resolved and has practical significance.Through studing this paper, we can eliminate some undesirable stationary points and make the the studing of the game theory is practical significance.