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

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