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 alpha-cores in finite coalition production economies with infinite-dimensional commodity spaces. As consequences, we obtain existence theorems for cores and alpha-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. (c) 2023 Elsevier B.V. All rights reserved.