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On characterization of equilibrium strategy of two-person zero-sum games with fuzzy payoffs. (English) Zbl 1065.91004
This is a very well written paper about equilibrium concepts in noncooperative two person games with “fuzzy payoffs”. Precisely, the author considers a model of a game in which players’ strategies are crisp, but the payoffs the players expect to get when their strategies are chosen are uncertain and, thus, represented by fuzzy numbers. This approach contrasts the model of a noncooperative game considered by D. Butnariu in [“Solution concepts for n-persons fuzzy games”, in Advances in Fuzzy Set Theory and Applications, M. M. Gupta, R. K. Ragade and R. R. Yager (eds.), North-Holland, 339–359 (1979; Zbl 0434.94026)] in which the expected payoffs are crisp, but their values depend on vague information involved in the decisional process. The author introduces meaningful equilibrium concepts for games with fuzzy payoffs and shows how the determination of such equilibria can be reduced to determining Nash equilibria in bimatrix games.
MSC:
91A10Noncooperative games
91A052-person games