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A Resolution Under Interval Uncertainty

Author

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  • Yan-An Hwang

    (Department of Applied Mathematics, National Dong Hwa University, 974 Hualien, Taiwan)

  • Yu-Hsien Liao

    (Department of Applied Mathematics & Green Nano Interdisciplinary Center (GNIC), National Pingtung University, 900 Pingtung, Taiwan)

Abstract

Traditional transferable utility (TU) games assume precise real-valued utilities for coalition outcomes, but real-world situations often involve uncertainty or imprecision. Interval TU games extend the classical framework by representing utilities and payoffs as closed intervals, leveraging interval arithmetic to address inherent ambiguities in data. This paper reviews the theoretical foundations of interval TU games and explores allocating solutions under uncertainty. Central to this study is the adaptation of consistency, a fundamental property in game-theoretical resolutions, to the interval framework. Drawing on concepts such as the pseudo equal allocations of non-separable costs and the pseudo weighted allocations of non-separable costs, we characterize these allocation resolutions through a specific reduction and related consistency. By bridging classical TU games with interval generalizations, this study offers a robust foundation for analyzing allocations under uncertainty and outlines avenues for future research in theoretical and applied game theory.

Suggested Citation

  • Yan-An Hwang & Yu-Hsien Liao, 2025. "A Resolution Under Interval Uncertainty," Mathematics, MDPI, vol. 13(5), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:762-:d:1599979
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    References listed on IDEAS

    as
    1. S. Alparslan-Gök & Silvia Miquel & Stef Tijs, 2009. "Cooperation under interval uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 99-109, March.
    2. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    3. Yan-An Hwang, 2009. "An NTU value under complement reduced game," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 305-324, November.
    4. Brânzei, R. & Dimitrov, D.A. & Pickl, S. & Tijs, S.H., 2002. "How to Cope with Division Problems under Interval Uncertainty of Claims?," Discussion Paper 2002-96, Tilburg University, Center for Economic Research.
    5. S. Zeynep Alparslan Gök & René van den Brink & Osman Palancı, 2024. "Moore interval subtraction and interval solutions for TU-games," Annals of Operations Research, Springer, vol. 343(1), pages 293-311, December.
    6. Yu-hsien Liao, 2010. "Value, complement reduction and interval TU games," Economics Bulletin, AccessEcon, vol. 30(4), pages 2671-2679.
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