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A graphical method for solving interval matrix games. (English) Zbl 1217.91006

Summary: \(2 \times n\) or \(m \times 2\) interval matrix games are considered, and a graphical method for solving such games is given. Interval matrix game is the interval generation of classical matrix games. Because of uncertainty in real-world applications, payoffs of a matrix game may not be a fixed number. Since the payoffs may vary within a range for fixed strategies, an interval-valued matrix can be used to model such uncertainties. In the literature, there are different approaches for the comparison of fuzzy numbers and interval numbers. In this work, the idea of acceptability index is used which is suggested by A. Sengupta, T. K. Pal and D. Chakraborty [Fuzzy Sets Syst. 119, No. 1, 129–138 (2001; Zbl 1044.90534)] and A. Sengupta and T. K. Pal [Fuzzy preference ordering of interval numbers in decision problems. Studies in Fuzziness and Soft Computing 238. Berlin: Springer (2009; Zbl 1169.90004)], and in view of acceptability index, well-known graphical method for matrix games is adapted to interval matrix games.

MSC:

91A05 2-person games
91A12 Cooperative games
91A99 Game theory
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