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Characterization of the equilibrium strategy of the bimatrix game with fuzzy payoff. (English) Zbl 0974.91004

This paper deals with bimatrix games with fuzzy payoff matrices. Two concepts of Nash equilibrium strategies are introduced and their properties are investigated. Finally the author gives an existence theorem of these Nash equilibrium strategies in any bimatrix game with fuzzy payoff.

MSC:

91A10 Noncooperative games
03E72 Theory of fuzzy sets, etc.
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[1] Aubin, J. P., Cooperative fuzzy game, Math. Oper. Res., 6, 1-13 (1981) · Zbl 0496.90092
[2] Aubin, J. P., Mathematical Methods of Games and Economic Theory (1979), North-Holland: North-Holland Amsterdam
[3] Buckley, J. J., Multiple goal non-cooperative conflicts under uncertainty: A fuzzy set approach, Fuzzy Sets and Systems, 13, 107-124 (1984) · Zbl 0549.90095
[4] Campose, L., Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets and Systems, 32, 275-289 (1989) · Zbl 0675.90098
[5] Dubois, D.; Prade, H., Ranking fuzzy numbers in the setting of possibility theory, Inform. Sci., 30, 183-224 (1983) · Zbl 0569.94031
[6] Fundenberg, D.; Tirole, J., Game Theory (1991), MIT Press: MIT Press Cambridge
[7] Kakutani, S., A generalization of Brouwer’s fixed point theorem, Duke Math. J., 8, 457-458 (1941) · JFM 67.0742.03
[8] Harsanyi, J., Games with incomplete information played by Bayesian players, Parts I, II, III, Manage. Sci., 14, 159-182 (1967-1968) · Zbl 0207.51102
[9] Mangasarian, O. L.; Stone, H., Two-person nonzero-sum games and quadratic programming, J. Math. Anal. Appl., 9, 348-355 (1964) · Zbl 0126.36505
[10] Owen, G., Game Theory (1982), Academic Press: Academic Press San Diego · Zbl 0159.49201
[11] Rosen, J. B., Existence and uniqueness of equilibrium points for concave n-person games, Econometrica, 33, 520-534 (1965) · Zbl 0142.17603
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