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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 {\it 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
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References:
[1] Aubin, J. P.: Mathematical methods of games and economic theory. (1979) · Zbl 0452.90093
[2] Aubin, J. P.: Cooperative fuzzy game. Math. oper. Res. 6, 1-13 (1984) · Zbl 0496.90092
[3] Campos, L.: Fuzzy linear programming models to solve fuzzy matrix games. Fuzzy sets and systems 32, 275-289 (1989) · Zbl 0675.90098
[4] Dubois, D.; Prade, H.: Systems of linear fuzzy constraints. Fuzzy sets and systems 3, 37-48 (1980) · Zbl 0425.94029
[5] Dubois, D.; Prade, H.: Ranking fuzzy numbers in the setting of possibility theory. Inform. sci. 30, 183-224 (1983) · Zbl 0569.94031
[6] Furukawa, N.: A parametric total order on fuzzy numbers and a fuzzy shortest route problem. Optimization 30, 367-377 (1994) · Zbl 0818.90136
[7] T. Maeda, Multi-objective Decision Making and Its Applications to Economic Analysis, Makino-syoten, 1996.
[8] Maeda, T.: Characterization of the equilibrium strategy of bi-matrix game with fuzzy payoff. J. math. Anal. appl. 251, 885-896 (2000) · Zbl 0974.91004
[9] Nash, J. F.: Equilibrium points in n-person games. Proc. nat. Acad. sci. 36, 48-49 (1950) · Zbl 0036.01104
[10] Nash, J. F.: Noncooperative games. Ann. of math. 54, 286-295 (1951) · Zbl 0045.08202
[11] Von Neumann, J.; Morgenstern, O.: Theory of games and economic behavior. (1944) · Zbl 0063.05930
[12] Ramı\acute{}k, J.; Řı\acute{}mánek, J.: Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy sets and systems 16, 123-150 (1985)
[13] Sakawa, M.; Yano, H.: Feasibility and Pareto optimality for multi-objective programming problems with fuzzy parameters. Fuzzy sets and systems 43, No. 1, 1-15 (1991) · Zbl 0755.90090