A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS - Cevikel, A. C.; Ahlatcioglu, M. (UNIV SISTAN & BALUCHESTAN, 2018)
In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs 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 payoffs 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 satisfies the superadditivity condition. Thus we considered a transition from two-person zero-sum games with fuzzy payoffs to cooperative games with fuzzy payoffs. The fair allocation of the maximum payoff (game value) of this cooperative game among players is done using the Shapley vector.
Keywords: Cooperative game; Fuzzy set; Fuzzy number; Shapley vector; Super-additivity; Zero-sum games; MULTIOBJECTIVE BIMATRIX GAMES; EQUILIBRIUM SOLUTIONS; Mathematics