Static Bayesian games with finite fuzzy types and the existence of equilibrium

This paper studies a special game with incomplete information, in which the payoffs of the players are both random and fuzzy. Such a game is considered in the context of a Bayesian game with the uncertain types characterized as fuzzy variables. A static fuzzy Bayesian game is then introduced and the decision rules for players are given based on credibility theory. We further prove the existence of the equilibrium of the game. Finally, a Cournot competition model with fuzzy efficiency under asymmetric information is investigated as an application and some results are presented.