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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Acknowledgments
This research was sponsored by the National Natural science Foundation of China (Nos. 71231003, 71171055), New Century Excellent Talents in University (the Ministry of Education of China, NCET-10-0020), Social Science Planning Project of Fujian (No. 2011C019, FJ2015B185), the Young and Middle-aged Teachers Education Scientific Research Project in Fujian Province (No. JA13392S), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20113514110009) and “Outstanding Young Scientific Research Personnel Cultivation Plan of Colleges and Universities in Fujian Province” as well as “Science and Technology Innovation Team Cultivation Plan of Colleges and Universities in Fujian Province”.
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Hong, FX., Li, DF. Nonlinear programming method for interval-valued n-person cooperative games. Oper Res Int J 17, 479–497 (2017). https://doi.org/10.1007/s12351-016-0233-1
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DOI: https://doi.org/10.1007/s12351-016-0233-1