Theory Study And Application On Shapley Value Of Repeated And Fuzzy Game

In game theory, solutions of cooperative game have been always a research focus. Shapley value has received attention more widely because it is based on marginal contribution and it is an exact value so that it can be well used into economics, politics and social science. With the development of game theory, repeated game and fuzzy game appeared, and the concepts and properties of its core, stable set had been studied, but the Shapley value of the repeated game and fuzzy game wasn't studied completely. The aim of this paper is to study the Shapley value for repeated game and fuzzy game systematically, then the Shapley value and its improved model are applied to solve the problem of profit allocation in supply chain.This paper can be divided into four chapters.First chapter is an introduction, it provide phylogeny of classical games theory, background and practical value of the paper.In the second part we introduce some basic concepts of repeated cooperative game theories firstly, arithmetic rules of coalition queue are defined, the carrier of coalition queue and three axioms of the Shapley value for repeated cooperative game are proposed, at last arithmetic formula and proof of the Shapley value for repeated cooperative game are given and analyzed by examples.In the third chapter some basic concepts of fuzzy cooperative game are introduced, fuzzy cooperative game with fuzzy coalition is mainly studied, character function is proposed according to the rates of player's participation, based on this character function, the Shapley value and its monotone, continuous properties for fuzzy cooperative game are given.In the last part we introduce the background of Supply chain and profit allocation in supply chain, the model of Shapley value is proposed according to fuzzy degree of participation, at the same time, the risk exists in the operation of supply chain, the evaluated model of inner risk is proposed, based on the inner risk, the model of Shapley value is given, and the model is applied to resolve the profit allocation in supply chain.