Dynamic production game with fuzzy demand in a supply chain

Dynamical game between multiple production firms in a supply chain wad studied in this paper. Considering the uncertainty of market demand, it was characterized as a fuzzy variable. And then the game between two firms and more than two ones was analyzed in the fuzzy environments. This paper defined expected Nash equilibrium of the game in the two cases. The existence of the Nash equilibrium was also proven. Due to the ability to solve production game in fuzzy environments, the proposed model had advantages over the existing ones in solving game of production fields. To illustrate the rationality and practicality of the proposed game model, a numerical example was given in the end.