Research On The Solutions Of Repeated Fuzzy Cooperative Games

In game theory, cooperative game has received a generous concern from scholars and become a research focus in academia. Half a century has passed, mature theory has been formulated in cooperative games. In 1974, Aubin put forth the idear of fuzzy cooperative game, after this,as an emerging branch of game theory—fuzzy game theory has attracted many scholar's interests. Recently scholars also conduct researches on various aspects of repeated games. Repeated non-cooperative games are studied by many scholars, and some significant results are obtained.The purpose of this paper is to further study the theory of fuzzy coalition game. By importing repeated cooperative game and compisite game to the fuzzy game, this paper studies the fuzzy games further, thus achieving the aim of perfecting the theory of the fuzzy games. The paper import the repeated cooperative game to the fuzzy game first, based on this, by importing the concept of the weak dominance, for the first time,we put forth the concept of weak dominance in the repeated fuzzy cooperative games. Further, for the first time, we define the weak core and the weak stable set of the repeated fuzzy cooperative game, and discuss the properties of them. Next, based on one kind of characteristic fuction of the fuzzy cooperative game which was define in a new way, the paper import the model of the non-negative linear compisite games to the fuzzy game, based on this, we study the shapley mapping of the fuzzy—non negative linear compisite games, thus making the theory of the fuzzy game more perfect.This paper is divided into four parts. The first part serves as an introduction, providing histories of classical games theory, background and practical value of the paper.In the second part we review the literature of some basic concepts of classic game theories, including core, stable set, kernel, nucleolus and the shapley of the cooperative game, and discuss the characteristics of them, and the relation between them.In the third part, we import the repeated game to the fuzzy game. For the first time, we put forth the concept of the weak dominance of the repeated fuzzy game, and based on this, for the first time we define the weak core and the weak stable set of the repeated cooperative game. Further,we study the properties of them.In the fourth part, we import the non-negative linear compisite game into the fuzzy game, based on one kind characteristic function of fuzzy game which was defined in a new way, we study the shapley mapping and the cumulative value of the fuzzy—non negative linear compisite games.