In this thesis,we mainly study the existence and stability of Nash equilibrium points in n-person non-cooperative game by further considering the rational behavior of players in the game model.First of all,in order to discuss the game problem without payment function,the generalized maximum element game model is introduced.In the framework of the generalized maximum element game,aiming at the barriers of players changing strategies in practical problems,the strategy transformation barrier function of players is introduced,the n-person non-cooperative game model with strategy transformation barriers is established,the concept of weak Nash equilibrium is put forward,and the existence of weak Nash equilibrium is discussed.This kind of game is extended to the case of generalized and generalized information sets.Based on the existence result of weak Nash equilibrium,the stability of weak Nash equilibrium is further discussed.Finally,in the bounded rationality model,the stability of the equilibrium set of n-person non-cooperative games with strategy transformation barriers is further studied,and the information set is introduced into the bounded rationality model,and the bounded rational behavior of players is attributed to the deviation caused by incomplete information,and it is proved that the set of equilibrium points of the bounded rational game based on the change of information state is stable in the sense of Baire classification.The full text is divided into five chapters,specifically as follows:The first chapter is the preface,which mainly introduces the research status of Nash equilibrium and the significance of studying weak Nash equilibrium.The second chapter is the preliminary knowledge,which mainly introduces the continuity of set-valued mappings,Fan-Glicksberg fixed point theorem and so on.The third chapter mainly studies the existence of weak Nash equilibrium,establishes the generalized maximal element game,by introducing the strategy transformation barrier function,the n-person non-cooperative game with strategy transformation barrier,the n-person non-cooperative generalized game with strategy transformation barrier and the n-person non-cooperative generalized information set game model with strategy transformation barrier are established.By defining the optimal response mapping,the existence of weak Nash equilibrium is proved by using Fan-Glicksberg fixed point theorem.The fourth chapter mainly studies the stability of the equilibrium set.By defining the corresponding game space and metric,it is obtained that there is at least one essential component in the equilibrium set.The fifth chapter mainly studies the stability of the equilibrium set in the game model under the condition of bounded rationality.By incorporating the strategy transformation barrier function into the bounded rationality function,the strategy transformation barrier of the player is regarded as the bounded rational behavior,and the stability of the weak Nash equilibrium is further discussed.it is proved that in the sense of Baire classification,M is structurally stable for most games ?(43)? and robust to ?-equilibrium.By introducing the information set into the bounded rationality model,the bounded rational behavior of players is attributed to the deviation caused by incomplete information,and it is proved that the set of equilibrium points of the bounded rational game based on the change of information state is stable in the sense of Baire classification. |