Research On The Solutions Of Repeated Fuzzy Cooperative Games

In game theory, cooperative game has received a generous concern and become aresearch focus in academia. Under the joint efforts of the majority of scholars at homeand abroad has witnessed the formation of the mature theory of cooperative game. Asan emerging branch of game theory, fuzzy game theory has attracted many scholar’sinterests since the last70’s. In recent years, repeated measures study step down bypeople, found it of great importance in application value, and so it has been a greatdeal of attention.The purpose of this paper is to further study and improved the theory ofcooperative game. Cooperation games on the basis of traditional solutions, byexpanding the solutions of the repeated fuzzy game, we present the new concepts ofthe repeated l-limit fuzzy cooperative game, and discuss the properties of them. Wecombine fuzzy game and repeated game, and establish the repeated fuzzy game model,and study the relations of the extended solutions of the repeated fuzzy game.This paper first serves as an introduction, providing histories of classical gamestheory, background and practical value of the paper.In the second, weak core, weak stable set and the nucleolus are defined on thebasic of relevant theory of the repeated fuzzy game, and establish the l-limit fuzzygame model, and we present the concepts of the weak core, weak stable set and thenucleolus of repeated l-limit fuzzy cooperative game, and discuss the properties ofthem.At last, we discuss basic concepts in cooperative game and present the newconcepts of extended core, extended stable set and extended nucleolus. Then repeatedgame introduced into the fuzzy game and expanded traditional solutions of repeatedfuzzy cooperative game. It is shown that the definitions and characters of extendedcore, extended stable set and extended nucleolus, the relations of solutions arediscussed.