A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core |
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| Authors: | Jiuqiang Liu Xiaodong Liu |
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| Institution: | 1. School of Management Engineering, Xi’an University of Finance and Economics, Xi’an Shaanxi, 710100, People’s Republic of China;2. Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA |
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| Abstract: | In 2004, Predtetchinski and Herings A. Predtetchinski, P.J.J. Herings, “A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game”, Journal of Economic Theory 116 (2004) 84–92] provided a necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game. In this paper, we extend this theorem to its counterpart in fuzzy games and give a necessary and sufficient condition for a non-transferable utility fuzzy game to have a non-empty fuzzy core. As a consequence, we derive a necessary and sufficient condition for non-emptiness of the fuzzy core of a TU fuzzy game. |
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| Keywords: | Cores Balanced collections π-balanced collections" target="_blank">gif" overflow="scroll">π-balanced collections Π-balanced collections" target="_blank">gif" overflow="scroll">Π-balanced collections TU games NTU games Fan&rsquo s Coincidence theorem Heine&ndash Borel finite cover theorem |
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