Several Solutions Of Fuzzy Cooperative Games

In game theory, Cooperative game has received a generous concern and become a research focus. The most extensively studied problem in cooperative game theory is how to divide the total earnings of the grand coalition if all players cooperate. Many solution concepts have been proposed to handle these problems, which satisfies a certain rational behavior and reasonable principle. As an emerging branch of game theory, fuzzy game theory has attracted many scholars' interest since the last 70's, some research results appeared one after another. The purpose of this paper is to extend mature theoretics of classic cooperative games to fuzzy coalition games by revising and perfecting, It affords theoretic bases for players to select coalitions in the game. So it has biggish applied value in modern time and it avoids unnecessary loss because of failure in selecting coalition.In classic cooperative games model, the prevenient literature has only considered the situation that coalitions among players are crisp, In fact the players' arbitrary subset as a feasible coalition is often inaccurate, so assumptions of classic cooperative games models are not applicable, the paper introduce fuzzy coalition games to deal solve uncertainty of coalition and extend the range of cooperation among players. In addition, it makes research and popularization of games solutions in concrete case more reasonable and more realistic.The paper can be divided into four chapters. First chapter is introduction, it provides development histories of classical games theory, background and practical value of the paper. In the second part we introduce some basic concepts of classic game theories first, In the following the problems such as core and stable set of TU fuzzy cooperative game, definition and properties of convex fuzzy coalition game, t - restricted fuzzy coalition game and so on are dealt with. In chapter III we expand repeated cooperative game theory to fuzzy space taking fuzzy coalition as a tool and establish repeated cooperative games model, thereby the concept of core and stable set are given, In the following the relations between them and properties of convex repeated cooperative games are considered. In the last part of the paper we deduce generalized core of big boss games by generalizing classic game in fuzzy condition. Then according to the upper and nether boundary, we can get a single solution~B-value (Ï„ style compromise value), lastly axiomatic characters of B-value are given.