Necessary and sufficient conditions for solutions of the Ky Fan minimax inequality and the non-emptiness of fuzzy cores in economies

In this paper, we provide a necessary and sufficient condition for the existence of solutions of the Ky Fan minimax inequality. We then apply this characterization to establish necessary and sufficient conditions for the non-emptiness of fuzzy cores and fuzzy α-cores in finite coalition production e...

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Bibliographic Details
Published in:Fuzzy sets and systems 2023-09, Vol.467, p.108580, Article 108580
Main Author: Liu, Jiuqiang
Format: Article
Language:English
Subjects:
Coalition production economy
Cores
Exchange economy
Fuzzy cores
Fuzzy α-cores
Ky Fan minimax inequality
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Summary:In this paper, we provide a necessary and sufficient condition for the existence of solutions of the Ky Fan minimax inequality. We then apply this characterization to establish necessary and sufficient conditions for the non-emptiness of fuzzy cores and fuzzy α-cores in finite coalition production economies with infinite-dimensional commodity spaces. As consequences, we obtain existence theorems for cores and α-cores which generalize corresponding results in the literature, in particular, we derive the non-emptiness of fuzzy cores in finite coalition production economies with upper semicontinuous (possibly discontinuous) utility functions and compact feasible commodity allocation sets.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2023.108580