Nash Balance Refinement Mechanism Based On Information Set

Game theory is a branch of operations research,in which non-cooperative game acts as a fundamental and key role.Moreover,the Nash equilibrium is the most important and central concept in the non-cooperative game theory.The achievement of Nash equilibrium generally depends on how players to speculate the common equilibrium points,because Nash equilibrium has the property of multiplicity and there are more than one or even innumerable equilibrium points,making it very difficult to speculate the common equilibrium points for players.Therefore,the refining of Nash equilibrium seems to be very important for game theory.In a game,players will grasp different information and may be affected or restricted by their knowledge structure or the objective environment.These different information status will affect the strategy selection of players,including strategy selection range and payment value.This will further leads to the change of information set,which affects the final outcome of the game.Thereby,it is very meaningful to explore the mechanism regarding on the Nash equilibrium refining based on the information set.In this thesis,we first establish the model of n people non-cooperative game within the information set and prove the existence theorem of Nash equilibrium fixed point in this model.Meanwhile,we establish the basic model of non-cooperative information set game based on partial order relationship,and prove the existence of Nash equilibrium in within information set game.In view of the change of information state,we further give an information set game model regarding the change of information state,as well as demonstrate the existence and stability of Nash equilibrium in information set game.In the third chapter of this thesis,in view of the influence of people in choosing strategies,we establish a general information set model that is different from the second chapter.The stability of the existence of Nash equilibrium in the information set game model are also discussed.Finally,we analyze the well-posedness of the solution set of bounded rationality and nonlinear problems,and proves the well-posedness of the generalized game underuncertainties and the well-posedness of the generalized multi-objective game under uncertainties.