The Expansion And Research On The Solutions Of Convex Stochastic Cooperative Games

The concern about game theory studies the interaction among multiple rationalparticipants and predicts their rational behavior to explore the equilibrium. For the reasonsof uncertainty of the payoffs and high complexity of decision actions, the convexstochastic cooperative games became the focus of research. Scholars have a series ofstudies about the stochastic cooperative games since Granot put the characteristic functioninto it and some good research results have been achieved.The thesis extended the convexstochastic cooperative games from three aspects: the uncertainty of payoffs, the payoffs ofcoalition,the convexity under certain conditions. The purpose of this paper is to extend theconvex stochastic cooperative game by revising and perfecting,so we can settle out thevalue of this game,it provides a powerful tool about uncertainty in reality.First of all, this paper provides the convex stochastic cooperative game and some ofits properties, for the aspects of core,by defining the concept of weakly dominant topropose the weak core and weak stable set for convex stochastic cooperative game.Theexistence and uniqueness of the weak core by using perference relation specific methodsare proved, which extends the theory of convex stochastic cooperative games solutions.This paper discusses the relationship between the weak core and weak stable set and to bedemonstrated.While the case that the core of game is empty proposed the concept ofbargaining set.And discussed the relationship between bargaining set and core under thecondition of convexity and to be demonstrated.Secondly, this paper extends the Shapley value and Banzhaf value axiomatization bythe bargaining power with different players. It proposes weight Shapley value and dummyabout axiomatization. Through establish the improved axiomatic system, And to study therelationship with the condition of convexity between the Shapley value and the classicalgames, discussed some of its properties and proved its feasibility and effectiveness. Andthe same time,this paper also investigates the properties of Banzhaf value under thecondition of convex linear extension,such as the feasibility and effectiveness,are discussedand proved.Then the modle of the uncertainty of payoffs on the transferable untility game is proposed. One out of a finite number of states of nature materializes and conditional onthe state, the players are involved in a particular transferable untility game. Wecharacterizes the weak sequential core and some of its properties and proves its existenceand its existence and its relationship to classical the convex transferable untility game.