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Linear programming approach to solve interval-valued matrix games

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  • Li, Deng-Feng

Abstract

Matrix game theory is concerned with how two players make decisions when they are faced with known exact payoffs. The aim of this paper is to develop a simple and an effective linear programming method for solving matrix games in which the payoffs are expressed with intervals. Because the payoffs of the matrix game are intervals, the value of the matrix game is an interval as well. Based on the definition of the value for matrix games, the value of the matrix game may be regarded as a function of values in the payoff intervals, which is proven to be non-decreasing. A pair of auxiliary linear programming models is formulated to obtain the upper bound and the lower bound of the value of the interval-valued matrix game by using the upper bounds and the lower bounds of the payoff intervals, respectively. By the duality theorem of linear programming, it is proven that two players have the identical interval-type value of the interval-valued matrix game. Also it is proven that the linear programming models and method proposed in this paper extend those of the classical matrix games. The linear programming method proposed in this paper is demonstrated with a real investment decision example and compared with other similar methods to show the validity, applicability and superiority.

Suggested Citation

  • Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.
  • Handle: RePEc:eee:jomega:v:39:y:2011:i:6:p:655-666
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    References listed on IDEAS

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    1. repec:eee:apmaco:v:273:y:2016:i:c:p:868-879 is not listed on IDEAS
    2. Li, Deng-Feng, 2012. "A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 223(2), pages 421-429.
    3. Ajay Kumar Bhurjee, 2016. "Existence of Equilibrium Points for Bimatrix Game with Interval Payoffs," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-13, March.
    4. Gong, Zaiwu & Xu, Xiaoxia & Zhang, Huanhuan & Aytun Ozturk, U. & Herrera-Viedma, Enrique & Xu, Chao, 2015. "The consensus models with interval preference opinions and their economic interpretation," Omega, Elsevier, vol. 55(C), pages 81-90.
    5. Chandra, S. & Aggarwal, A., 2015. "On solving matrix games with pay-offs of triangular fuzzy numbers: Certain observations and generalizations," European Journal of Operational Research, Elsevier, vol. 246(2), pages 575-581.

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