Aubin cores and bargaining sets for convex cooperative fuzzy games |
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Authors: | Wenbo Yang Jiuqiang Liu Xiaodong Liu |
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Affiliation: | 1.Department of Applied Mathematics,School of Science Northwestern Polytechnical University,Xi’an,People’s Republic of China;2.School of Management Engineering,Xi’an University of Finance and Economics,Xi’an,People’s Republic of China;3.Department of Mathematics,Eastern Michigan University,Ypsilanti,USA |
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Abstract: | In this paper, we deal with Aubin cores and bargaining sets in convex cooperative fuzzy games. We first give a simple and direct proof to the well-known result (proved by Branzei et al. (Fuzzy Sets Syst 139:267–281, 2003)) that for a convex cooperative fuzzy game v, its Aubin core C(v) coincides with its crisp core C cr (v). We then introduce the concept of bargaining sets for cooperative fuzzy games and prove that for a continuous convex cooperative fuzzy game v, its bargaining set coincides with its Aubin core, which extends a well-known result by Maschler et al. for classical cooperative games to cooperative fuzzy games. We also show that some results proved by Shapley (Int J Game Theory 1:11–26, 1971) for classical decomposable convex cooperative games can be extended to convex cooperative fuzzy games. |
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