A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS

Abstract

In this paper, we deal with games with fuzzy payoffs. We proved that players<br /> who are playing a zero-sum game with fuzzy payoffs against Nature are able<br /> to increase their joint payoff, and hence their individual payoffs by<br /> cooperating. It is shown that, a cooperative game with the fuzzy<br /> characteristic function can be constructed via the optimal game values of<br /> the zero-sum games with fuzzy payoffs against Nature at which players'<br /> combine their strategies and act like a single player. It is also proven<br /> that, the fuzzy characteristic function that is constructed in this way<br /> satisfies the superadditivity condition. Thus we considered a transition<br /> from two-person zero-sum games with fuzzy payoffs to cooperative games with<br /> fuzzy payoffs. The fair allocation of the maximum payoff (game value) of<br /> this cooperative game among players is done using the Shapley vector.