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 witnessed the formation of the mature theory of cooperative game. As an emerging branch of game theory, fuzzy game theory has attracted many scholars' interest since the last 70's, which results in research findings one after another. 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 expanding the definition of dominance, we present the new concepts of weak core and weak stable set, and discuss the properties of them. We combine fuzzy game and repeated game, and establish the sum-compound repeated fuzzy game model, and study the relations of the core and stable set of the game and the cores and stable sets of the compound games.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, Shapley function, bargaining set, weak dominance and stable set. We discuss the properties of these solutions of TU cooperative game.In the third part we discuss basic concepts in fuzzy game and introduce new definitions of weak dominance and weak sable set for fuzzy game. We highlight the study of convex fuzzy game in terms of its unique and crucial features.In the last part we employ the concept of sum-compound repeated fuzzy cooperative game, define stable set of this game with fuzzy coalition and study the relations between the core and stable set of sum-compound repeated fuzzy game and the cores and stable sets of compounded games.