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Nonlinear programming method for interval-valued n-person cooperative games

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  • Fang-Xuan Hong

    (Fuzhou University
    Fuzhou University)

  • Deng-Feng Li

    (Fuzhou University)

Abstract

The aim of this paper is to develop a nonlinear programming method for computing the elements of the interval-valued cores of n-person cooperative games in which coalitions’ values are expressed with intervals, which are often called interval-valued n-person cooperative games for short. With finding out the maximum satisfactory degree in the situation with the features of inclusion and/or overlap relations between intervals, this paper tries to explore the cooperation chance in this type of cooperative games. Firstly, we define the concept of interval-valued cores of interval-valued n-person cooperative games and satisfactory degrees (or ranking indexes) of comparing intervals with the features of inclusion and/or overlap relations. Hereby, we propose the auxiliary nonlinear programming model and method for solving interval-valued cores of any interval-valued n-person cooperative games. The developed method can provide cooperative chance under the situation of inclusion and/or overlap relations between intervals, while the traditional interval ranking method may not assure that the interval-valued cores exist. This method is a complement to the traditional methods rather than the alternative one. The feasibility and applicability of the model and method proposed in this paper are illustrated with a numerical example.

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  • Fang-Xuan Hong & Deng-Feng Li, 2017. "Nonlinear programming method for interval-valued n-person cooperative games," Operational Research, Springer, vol. 17(2), pages 479-497, July.
    • Handle: RePEc:spr:operea:v:17:y:2017:i:2:d:10.1007_s12351-016-0233-1
    DOI: 10.1007/s12351-016-0233-1
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    1. Hsien-Chung Wu, 2018. "Interval-Valued Cores and Interval-Valued Dominance Cores of Cooperative Games Endowed with Interval-Valued Payoffs," Mathematics, MDPI, vol. 6(11), pages 1-26, November.

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