Research On The Solutions Of Interval Cooperative Games And Its Expansion

Game theory provides a theoretical foundation and methods for study the interactionbetween people. For the reasons of uncertainty of environments and high complexity ofdecision actions, fuzzy extension of cooperative games became the focus of research.Scholars have a series of studies about fuzzy cooperative games since it emerged in1970’s.Recent years, interval cooperative games become a new direction of game theory, haveattracted many scholars’ interests, and some results have achieved already.The thesis extended interval cooperative games model from three aspects: preferencerelation of the players about payoffs, the coalition structure and alliance payoffs as a fuzzynumber. The purpose of this paper is to improve interval cooperative games theory, andprovide a powerful tool to deal with the reality of uncertainty phenomenon.The main contributions of this dissertation are as follows:Firstly, based on the core of multiple scenario cooperative games, the interval coreand interval P-core of interval cooperative games are defined, and the relationshipbetween these solutions is given. The algorithm for computing an element in the intervalcore is also given. In order to avoid overlooking the fuzzy information which contained inthe interval data, the preference relations of players about payoffs is defined. The intervalcore of interval cooperative games with the player have same preferences is studied.Secondly, consider the limitation of the coalition, established interval cooperativegame on augmenting systems, a particular coalition structure. Based on the properties ofaugmenting systems, the interval Shapley value of this model is defined. The axiomssystem of this interval Shapley value is given, existence and uniqueness of the intervalShapley value is proved. Then, we give the interval Shapley value determination of profitdistribution scheme when the alliance payoffs is relatively accurate.Thirdly, through the establishment of the axioms system, put forward the concept ofthe Shapley-like value of cooperative games with fuzzy payoffs. And on this basis, wedefine the fuzzy Shapley value with a new method. Some properties of the fuzzy Shapleyvalue are given. According to the existence conditions of interval Shapley value, we obtained the conditions for the existence of the fuzzy Shapley value. The fuzzy Shapleyvalue when the payoffs function of cooperative games is given by the trapezoidal fuzzynumber is discussed.