| Recently,essential components of solution set is an important aspect of stability for nonlinear problems. It plays a crucial role in the study of stability of optimal solutions,Nash equilibrium and fixed points of mapping. In this paper, we will base on the existence of strongly essential set and strongly essential component of set-valued mapping about the mixedδ-perturbation and around the gerneralized imformation sets game, then discuss the stability of the Nash equilibrium.In the chapter one, we will construct the model of generalized information sets game and prove the existence it's equilibrium. Base on this,we will discuss the existence of strongly essential set and essential set under the condition of both the pay off functions and the imformation-districted mapping have perturbation and the imformation-districted mapping, the imformation state and the pay off functions were all perturbating ,respectively. And we prove the existence of the essential component. That is, around the former two conditions, we will show that the generalized information set game has at least one strongly essential component and essential component of it's Nash equilibrium points sets.In the chapter two, we will use some result of stability of the Nash equilibrium of the generalized information set game of chapter one. Further, we discuss the stability of the Nash equilibrium of the generalized information set game and the n-person noncooperative finite game. At first,use the special forms of the imformation-districted mapping of the generalized information set game, we will give some results about the Nash equilibrium of the generalized game;second,under the significance of strategic set's perturbation, we will discuss the existence of the strategic essential set,strategic stable set and strategic essential component of the Nash equilibrium sets of the n-person noncooperative general game;finally,we discuss the result of CKM equilibrium of n-person noncooperative finite game. |
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