Research On The Solutions Of Repeated Fuzzycooperative Games

In game theory, cooperative game has received a generous concern from scholars andbecome a research focus in academia. Half a century has witnessed the formation of themature theory of cooperative game. As an emerging branch of game theory,fuzzy gametheory has attracted many scholar's interests since the last70's. Recently scholars alsoconduct researches on various aspects of repeated games. Repeated non-cooperativegames are studied by many scholars, and some significant results are obtained.The purpose of this paper is to further study the theory of cooperative game. Byexpanding the definition of the traditional solutions of the cooperative game, we presentthe new concepts of interval fuzzy solutions, and discuss the properties of them. Wecombine fuzzy game and repeated game, and establish the repeated fuzzy game model,and study the extended solutions of the fuzzy cooperative game and repeated fuzzy game.Firstly, serves as an introduction, providing histories of classical games theory,background and practical value of the paper.Secondly, interval fuzzy Shapley value and interval fuzzy stable set are defined onthe basic of relevant theory of fuzzy mathematics. We discuss the properties of theseinterval fuzzy solutions. And a practical example of interval fuzzy stable set is provided toillustrate the validity and feasibility.Finally, taking fuzzy coalition as a tool, we expanded traditional solutions of fuzzycooperative game and repeated fuzzy cooperative game. And we present the new conceptsof extended core, extended stable set, extended Ï„-core and so on. Eventually, therelations and properties of solutions are discussed.