Research On The Static Bayesian Games With Finite Fuzzy Types And Its Application

This thesis studies a new kind of game with fuzzy incomplete infbrmation.In this thesis,we characterize the possible types of the players in the incomplete infbrmation game as fuzzy variables and build a static Bayesian game with fuzzy types.To analysis such game,firstly the definition of fuzzy mapping is proposed. Then the continuity and convexity of the expected value function of a fuzzy mapping are studied.These results are used to analysis the Bayesian game in a fuzzy environment.By giving the definitions of fuzzy type,strategy and belief, the static fuzzy Bayesian game with finite type is defined.The characterization of the equilibrium of this game is considered,and a sufficient condition for the existence of the equilibrium is given.Mechanism design is a way to design the rule of a game such that players' selfishness leads to the welfare of the group.In this thesis,the mechanism design problem under a fuzzy environment is studied and the definition of static fuzzy Bayesian Nash implement is proposed.To clarify, this thesis considers three models for application:retailer's optimization problem with fuzzy selling ability;a Cournot competition model with fuzzy efficiency under asymmetric infbrmation and the production contract selection model under a fuzzy environment.