Research On The Solution Of Fuzzy Cooperative Game

Half a century has witnessed the formation of the mature theory of classic cooperative game. The most studied problem in the cooperative game is the study of game theory in uncertain circumstance. The fuzzy cooperative game is one of its studies. As an emerging branch of game theory, fuzzy game theory has attracted quite a few scholars' interest since the last 70s'. A few study achievements appeared. Its studies focus on the solutions of games uncertainty in the degree of participation of players in a coalition and fuzziness in the characteristic function. For these two studies, people put forward to all sorts of solution concepts, but everyone to satisfy the individual rationality and the group rationality. Cooperative games with fuzzy coalitions and fuzzy characteristic function are separately studied in the literature.In this paper we define the strongεcore of the fuzzy coalition Cooperative games and repeated fuzzy coalition cooperative games, with fuzzy coalitions and the core of fuzzy cooperative games and repeated fuzzy cooperative games, then in theory the shortcomings of empty core were compensated. The strongεcore is multiple-valued solution, due to its set-valued nature, still can not determine the specific allocation of the players of game. In this paper we define theτ-value on fuzzy coalition cooperative games and nucleolus on fuzzy characteristic function cooperative games as a single-value solution.This paper can be divided into four chapters. First chapter is introduction, it provide phylogeny of classical games theory, background and practical value of the paper. In the second part we define the strongεcore and theτ-value of fuzzy coalition cooperative games, and then the properties of strongεcore andτ-value was given. In the third chapter we define the strongεcore of repeated fuzzy coalition cooperative games, and then the character of strongεcore was given. In the last part of the paper we introduce the core, nucleolus and kernel of fuzzy characteristic function, and then the relation among solutions were shown, and gives a specific example seeking nucleolus.