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Matrix games with payoffs of belief structures

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  • Deng, Xinyang
  • Liu, Qi
  • Deng, Yong

Abstract

Imprecise matrix games, such as interval-valued matrix games and fuzzy matrix games, have attracted much interest for a long time. Most of the previous studies on imprecise matrix games mainly focus on the fuzzy uncertainty of payoffs. However, the uncertainties of nonspecificity and discord involved in payoffs are not well addressed so far. The purpose of this paper is to study the matrix game with such types of uncertainties. In order to achieve that purpose, we present a matrix game model with payoffs of belief structures so as to integrate discord and nonspecificity. The proposed model can be used to express more imprecise interactions between players in the reality. Besides, as another main contribution of the study, an effective method for solving matrix games with belief structures payoffs is developed to help us find the equilibrium points of the kind of games. At last, an example is given to illustrate the proposed model and method.

Suggested Citation

  • Deng, Xinyang & Liu, Qi & Deng, Yong, 2016. "Matrix games with payoffs of belief structures," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 868-879.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:868-879
    DOI: 10.1016/j.amc.2015.10.056
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    References listed on IDEAS

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    1. Xinyang Deng & Yong Deng & Felix Chan, 2014. "An improved operator of combination with adapted conflict," Annals of Operations Research, Springer, vol. 223(1), pages 451-459, December.
    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. Prasun Kumar Nayak & Madhumangal Pal, 2009. "Linear Programming Technique To Solve Two Person Matrix Games With Interval Pay-Offs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(02), pages 285-305.
    4. Alessandro Di Mare & Vito Latora, 2007. "Opinion Formation Models Based On Game Theory," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(09), pages 1377-1395.
    5. Deng, Xinyang & Hu, Yong & Chan, Felix T.S. & Mahadevan, Sankaran & Deng, Yong, 2015. "Parameter estimation based on interval-valued belief structures," European Journal of Operational Research, Elsevier, vol. 241(2), pages 579-582.
    6. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.
    7. Vijay, V. & Chandra, S. & Bector, C.R., 2005. "Matrix games with fuzzy goals and fuzzy payoffs," Omega, Elsevier, vol. 33(5), pages 425-429, October.
    8. 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.
    9. Sang-Bing Tsai & Min-Fang Chien & Youzhi Xue & Lei Li & Xiaodong Jiang & Quan Chen & Jie Zhou & Lei Wang, 2015. "Using the Fuzzy DEMATEL to Determine Environmental Performance: A Case of Printed Circuit Board Industry in Taiwan," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-18, June.
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    Cited by:

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    5. Yin, Likang & Zheng, Haoyang & Bian, Tian & Deng, Yong, 2017. "An evidential link prediction method and link predictability based on Shannon entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 699-712.

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