PN equilibrium strategy for matrix games with fuzzy payoffs

Considering the fact that the players may have different risk attitudes for the approximate values of strategies, this paper uses the possibility and necessity measures to denote the risk attitudes of the players, which are useful tools to address this issue. To do this, the concepts of possibility and necessity expectations of fuzzy variables are introduced, and several desirable properties are studied. Then, two vectors to denote the players' risk attitudes for their strategies are presented. Furthermore, the concept of possibility and necessity (PN) equilibrium strategy is defined, and the associated models are constructed, by which the optimal possibility and necessity equilibrium strategy is obtained. Meanwhile, a special case is briefly considered. Finally, a numerical example is offered to show the equilibrium strategy of the players.