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Bilinear Programming Approach to Solve Interval Bimatrix Games in Tourism Planning Management

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Abstract

The bimatrix game theory concerns 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 bilinear programming method for solving bimatrix games with payoffs expressed by intervals, which are called interval bimatrix games for short. In this method, the values of players are regarded as functions of the values in the payoff intervals, which are of monotonicity. Hereby, we construct a pair of auxiliary bilinear programming models, which are used to explicitly compute the upper and lower bounds of the interval values of players in any interval bimatrix game by, respectively, using the lower and upper bounds of the payoff intervals and corresponding optimal strategies. The validity and applicability of the models and method proposed in this paper are illustrated with a real example of the tourism planning management problem.

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Acknowledgments

This research was sponsored by the Key Program of the National Natural Science Foundation of China (No. 71231003), the National Natural Science Foundation of China (No. 71171055), the Social Science Planning Project of Fujian Province (No. 2013B053), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20113514110009) as well as “Science and Technology Innovation Team Cultivation Plan of Colleges and Universities in Fujian Province.”

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Authors and Affiliations

  1. School of Architecture, Fuzhou University, Fuzhou, Fujian, 350108, China

    Wei Fei

  2. School of Economics and Management, Fuzhou University, Fuzhou, Fujian, 350108, China

    Deng-Feng Li

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  1. Wei Fei
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  2. Deng-Feng Li
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Correspondence to Deng-Feng Li.

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Fei, W., Li, DF. Bilinear Programming Approach to Solve Interval Bimatrix Games in Tourism Planning Management. Int. J. Fuzzy Syst. 18, 504–510 (2016). https://doi.org/10.1007/s40815-015-0082-8

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  • DOI: https://doi.org/10.1007/s40815-015-0082-8

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