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

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  • Qi-Qing Song
  • Jia-Lin Liu
  • Jia-Yu Cui

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-$\pi$-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.

Suggested Citation

  • Qi-Qing Song & Jia-Lin Liu & Jia-Yu Cui, 2026. "Non-emptiness of the Fuzzy Core for Exchange Economies with Discontinuous Utility," Papers 2610.06572, arXiv.org.
    • Handle: RePEc:arx:papers:2610.06572
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    References listed on IDEAS

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