Research On The Solutions Of Grey Cooperative Games

Game theory provides a theoretical foundation and methods for study the interaction between people. For the reasons of high complexity of decision actions and uncertainty of environments, fuzzy extension of cooperative games became the focus of research. Some scholars have a series of studies about fuzzy cooperative games since it emerged in 1970’s. Recent years, games theory with grey in information become a new direction of game theory, have attracted many scholars interests, and some results have achieved already.This dissertation incestigats systematically the main conclusion of the nucleolus solution of the grey pay cooperative games, as well as the grey core and grey stable set of the interval grey cooperative games, as well as the core and stable set of the convex compound grey cooperative games, and gives the solving method of the nucleolus solution of the grey pay cooperation games. The main contributions of this dissertation are as follows:Firstly, the problem of a cooperative game with payoffs of grey sets(GS) and its nucleolus solution are studied. In this methodology, the mathematical expression of the model of the grey pay cooperative games is formulated. The concept of its solutions is defined and the properties are investigated. A new ranking method is proposed. Based on the new ranking approach, the grey nucleolus can be obtained by solving the bi-objective nonlinear programming model. The relationship between the solutions of the model is analyst, and the main conclusions are given.Secondly, the problem of a cooperative game with grey coalition and the solutions are studied. The model of the cooperative games with grey coalition and payoffs of grey sets is established, and the interval grey core and interval stable sets of the games are obtained, as well as the relationship with subinterval grey games. Forthermore, through the analysis, it is concluded that the grey alliance is the extension of the fuzzy alliance.Thirdly, based on the model of the grey cooperative games, the interval convex compound grey cooperative games with grey coalition and the solutions are studied. In this methodology, the mathematical expression of the model of the interval convex compound grey cooperative games is formulated. The related definitions about that model and the concept of its solutions are defined. Then some characters and properties of this kinds of solutions are given.