Research On The Solutions Of Convex Compound Stochastic Cooperative Games

In game theory, cooperative game has received a concern and become a researchfocus. Stochastic cooperative game, as a branch of game theory, it has attracted manyscholars'interest, and some significant results are obtained.The main paper is the stochastic cooperative game model by adding convexcompound game theory, set up convex compound stochastic cooperative game, under thecondition in the stochastic cooperative game, introduce their convexity and superadditive,we present the new concepts of kernel,nucleolus and Shapley value, and discuss theproperties of them. Then we combine the convex compound game and stochasticcooperative game, give their structure of nucleolus, core and stable set, and by expandingthe definition of dominance, we present the new concepts of weak core and weak stableset, study their properies and the relations of the core and stable set.First, providing histories of classical games theory, background and practical value ofthe paper.Second, introduce the stochastic cooperative game which related to the thesis,introduce the convexity and superadditive of the stochastic cooperative game, focusing ontheir concepts and characteristics of kernel and nucleolus for the following.In the last part, we define the convex compound stochastic cooperative game model,define the concept of core, strong ε-core and stable set, study the properties of them, thengive the relations between the core and stable set. Then we define the weak dominance,give the concepts of weak core and weak stable set, and the relations between them.