N-Person Credibilistic Non-cooperative Game with Fuzzy Payoffs

Abstract

In real game situations, the players are often lack of the information about their opponents’ or even their own payoffs. The existing literature on non-cooperative games with uncertain payoffs just focused on two-person zero-sum games or bimatrix games. In this paper, we consider a n-person non-cooperative game with fuzzy payoffs. First, based on credibility theory, three credibilistic criteria are introduced to define the behavior preferences of players in different game situations. Then, three solution concepts of credibilistic equilibria and their existence theorems are proposed. Finally, three sufficient and necessary conditions are presented for finding the credibilistic equilibrium strategies to illustrate the usefulness of the theory developed in this paper.