Research On Solutions Of Rough Cooperative Games

Game theory is an important theory of rational interaction between participants in research institutes,and research on games in uncertain environment has gradually become the focus issue.One of the most typical is the fuzzy game,a series of research results have emerged,has developed into a more mature theory.In recent years,the emergence of rough game theory has become a new direction for the study of game theory.The rough set theory has been introduced into game research by a large number of scholars to solve the problem of incomplete and inaccurate information and corresponding research results have been achieved.In this paper,combining the theory of rough set and cooperative game,the fuzzy cooperative game model with payoffs as an interval rough number is established and its various solutions are studied.The main contents of the thesis are as follows:Firstly,the Shapley value of cooperative games with the interval rough payoff value is studied.Based on fuzzy cooperative game model and interval rough theory,a cooperative game model with interval rough payoff is constructed.The axiom of Shapley value in the classical sense is extended and the related properties of Shapley function in this form are proved.Due to the irreversibility of the subtraction of the interval rough number,the interval rough fuzzy Shapley value is defined by the improved algorithm.Combined with the average distribution function,the interval Shapley value is defined,which is a further expansion of the interval Shapley value.Secondly,based on the nature of the binding of the players in the game and the uncertainty of the revenue,an interval rough payoff cooperative game model is established on augmenting systems with a coalition structure,and the specific form of the rough Owen value of the model is given.The corresponding expressions are analyzed,and the validity of the rough Owen value is verified by an example.Finally,aiming at the situation of interval rough payoff cooperative game in which the players in the game cooperate with some degree of participation,a rough payoff cooperative game model with fuzzy coalition is established.The rough core of the fuzzy cooperative game is defined,and the core non-empty conditions are given.The relationship between the rough core and the normal rough core and the dominated rough core is discussed and proved.Another example is to verify the validity and feasibility of this rough core.