Existence of an Aumann–Maschler fuzzy bargaining set and fuzzy kernels in TU fuzzy games

In this paper, we first give fuzzy extensions of the well-known solution concepts of kernel and prekernel for a transferable utility (TU) game and establish the existence of fuzzy kernels in TU fuzzy games which generalizes the corresponding result for classical TU games by Davis and Maschler [5]. W...

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Bibliographic Details
Published in:Fuzzy sets and systems 2018-10, Vol.349, p.53-63
Main Authors: Liu, Jiuqiang, Liu, Xiaodong, Huang, Yan, Yang, Wenbo
Format: Article
Language:English
Subjects:
Bargaining sets
Cores
Fuzzy kernels
Fuzzy prekernels
TU fuzzy games
TU games
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Summary:In this paper, we first give fuzzy extensions of the well-known solution concepts of kernel and prekernel for a transferable utility (TU) game and establish the existence of fuzzy kernels in TU fuzzy games which generalizes the corresponding result for classical TU games by Davis and Maschler [5]. We then prove that the fuzzy kernel is a subset of the fuzzy bargaining set in a TU fuzzy game, which gives the fuzzy counterpart of the corresponding fact for classical TU games by Davis and Maschler. As a consequence, we establish the existence of fuzzy Aumann–Maschler fuzzy bargaining sets for TU fuzzy games which generalizes the well-known existence theorem for bargaining sets by Aumann and Maschler [1] and Peleg [11].
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2018.01.010