Abstract
This paper is mainly to discuss cooperative games on convex geometries with a coalition structure, which can be seen as an extension of cooperative games with a coalition structure. For this kind of games, the cooperation among unions and within each union will be the convex sets, i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively. The explicit form of the generalized Owen value for this kind of games is given, which can be seen as an extension of the Owen value. Furthermore, two special cases of this kind of games are researched. The corresponding payoff indices are also studied. Finally, an illustrative example is given.
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This work was supported by the National Natural Science Foundation of China under Grant Nos. 71201089, 71271217, and 71071018, and the Natural Science Foundation of Shandong Province, China, under Grant No. ZR2012GQ005.
This paper was recommended for publication by Editor Shouyang WANG.
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Meng, F., Zhang, Q. Cooperative games on convex geometries with a coalition structure. J Syst Sci Complex 25, 909–925 (2012). https://doi.org/10.1007/s11424-012-0298-8
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DOI: https://doi.org/10.1007/s11424-012-0298-8