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

Fang-Xuan Hong and Deng-Feng Li ()
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Fang-Xuan Hong: Fuzhou University
Deng-Feng Li: Fuzhou University

Operational Research, 2017, vol. 17, issue 2, No 6, 479-497

Abstract: 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.

Keywords: Cooperative game; Interval-valued core; Interval ranking; Mathematical programming; Management (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s12351-016-0233-1

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