According to the definition of Nash equilibrium, the player can not change his own strategy alone to make his own payment larger，this paper puts forward a new kind of equilibrium, which is that the player can really increase his own payment by changing his own strategy.Because of the fact that the player’s change of strategy will produce cost,however，when the cost is higher than or equal to the increased payment, the player does not change his strategy. Based on this factual background, the cost function of players is introduced into the game model, the n-person non-cooperative game model and n-person non-cooperative generalized game model are reestablished, and the definition of weak Nash equilibrium point is given. On this basis, the existence of weak Nash equilibrium in the game model is studied. By defining the optimal response mapping, it is proved that the optimal response mapping is usco, non-empty and convex by using the correlation lemma. The existence of weak Nash equilibrium point of n-person non-cooperative game and n-person non-cooperative generalized game is proved by Fan-Glicksberg fixed point theorem.