On characterization of credibilistic equilibria of fuzzy-payoff two-player zero-sum game

Harsanyi pointed out that "the player may lack full information about the other players' (or even his own) payoffs, etc." In this paper, we investigate the two-player zero-sum game, in which the payoffs are interpreted as fuzzy variables due to incomplete information. Based on the credibility theory, we employ three decision criteria to define the behaviors of the players in different decision situations. Accordingly, three definitions of Nash equilibria, called credibilistic equilibria, are proposed. Besides the existence theorem of the three credibilistic equilibria, we also discuss their relationships to illustrate the significance of the proposed credibilistic equilibria.