Credibility Theory Based Strategic Problems On Game

Because of the complexity of the actual game environment,the related information of the players' thinking is fuzzy.The players always take part in the game with subjective thinking,which makes the whole game process fuzzy.the payoffs of people is a fuzzy variable in the complex decision-making environment,which provides a reasonable and effective method for dealing with incomplete and uncertain game problems.This paper introduces the research background and current situation of game theory,credibility theory,credibilistic non-cooperative game and credibilistic coalitional game,and summarizes the concepts of credibility measure,four criteria of comparative fuzzy variables,n-person credibilistic strategy game and coalitional game with fuzzy transferable payoff.The specific research work is as follows:Firstly,the paper investigates n-person strategic game with fuzzy payoffs,which are viewed as fuzzy variable because of incomplete information.Based on the credibility theory,fuzzy ranking methods are introduced to characterize the behaviors of players in different decision situations.Accordingly,four credibilistic equilibria are defined,equivalent to Nash equilibria.Next,theorems are given to confirm the existence of these credibilistic equilibria.Numerical example is used to illustrate the significance of four credibilistic equilibria in practical strategic games.Moreover,we also discuss their relationships of four credibility equilibria.Secondly,the paper investigates fuzzy coalitional game.Coalitional payoffs are viewed as fuzzy variable because of uncertain information.Based on the credibility theory,fuzzy ranking methods are introduced to characterize the behaviors of players in different decision situations.Accordingly,two kinds of credibilistic nucleolus are defined,which include expected nucleolus and optimistic nucleolus.Two kinds of credibilistic shapley values are defined,which include expected shapley values and optimistic shapley values,namely,the solutions of fuzzy coalitional game.Existence and uniqueness theorem of new solutions are given to confirm respectively.Numerical example is used to illustrate the significance of the theory developed in practical fuzzy coalitional games,and we also discuss their relationships between two kinds of credibilistic nucleolus(credibilistic shapley value).Finally,this part is a conclusion,which explains the advantages and disadvantages of credibilistic game,and puts forward the prospect.