Necessary and sufficient conditions for solutions of the Ky Fan minimax inequality and the non-emptiness of fuzzy cores in economies
Document Type
Article
Publication Date
2023
Department/School
Mathematics
Publication Title
Fuzzy Sets and Systems
Abstract
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.
Link to Published Version
Recommended Citation
Liu, J. (2023). Necessary and sufficient conditions for solutions of the Ky Fan minimax inequality and the non-emptiness of fuzzy cores in economies. Fuzzy Sets and Systems, 467, 108580. https://doi.org/10.1016/j.fss.2023.108580
Comments
J. Liu is a faculty member in EMU's Department of Mathematics and Statistics.