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arXiv · 2610.06572

Non-emptiness of the Fuzzy Core for Exchange Economies with Discontinuous Utility

Qi-Qing Song·Jia-Lin Liu·Jia-Yu Cui
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Abstract

This paper investigates the non-emptiness of the fuzzy core and introduces the notion of the TU-fuzzy core for pure exchange economies with discontinuous utility functions. We propose two stability conditions: local fuzzy-coalition stability and local TU-fuzzy-coalition stability. We also introduce an independent-$π$-balanced family of subsets of the agent set to construct two payoff-dependent NTU games. These constructions serve as bridges linking the fuzzy core, the TU-fuzzy core, and NTU games. Under the proposed stability conditions, we establish the non-emptiness of the fuzzy core for economies with quasi-concave utility functions and the non-emptiness of the TU-fuzzy core for economies with concave utility functions.

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Qi-Qing Song, Jia-Lin Liu, Jia-Yu Cui. 2026-10-05. Non-emptiness of the Fuzzy Core for Exchange Economies with Discontinuous Utility. https://arxiv.org/abs/2610.06572

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