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The interval Shapley value: an axiomatization

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  • S. Alparslan Gök
  • R. Branzei
  • S. Tijs

Abstract

The Shapley value, one of the most widespread concepts in operations Research applications of cooperative game theory, was defined and axiomatically characterized in different game-theoretic models. Recently much research work has been done in order to extend OR models and methods, in particular cooperative game theory, for situations with interval data. This paper focuses on the Shapley value for cooperative games where the set of players is finite and the coalition values are compact intervals of real numbers. The interval Shapley value is characterized with the aid of the properties of additivity, efficiency, symmetry and dummy player, which are straightforward generalizations of the corresponding properties in the classical cooperative game theory. Copyright Springer-Verlag 2010

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  • S. Alparslan Gök & R. Branzei & S. Tijs, 2010. "The interval Shapley value: an axiomatization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(2), pages 131-140, June.
    • Handle: RePEc:spr:cejnor:v:18:y:2010:i:2:p:131-140
    DOI: 10.1007/s10100-009-0096-0
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    7. Yan-an Hwang & Ming-chuan Chen, 2012. "A new axiomatization of the Shapley value under interval uncertainty," Economics Bulletin, AccessEcon, vol. 32(1), pages 799-810.
    8. Yu, Xiaohui & He, Mingke & Sun, Hongxia & Zhou, Zhen, 2020. "Uncertain coalition structure game with payoff of belief structure," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    9. Deng-Feng Li & Yin-Fang Ye, 2018. "Interval-valued least square prenucleolus of interval-valued cooperative games and a simplified method," Operational Research, Springer, vol. 18(1), pages 205-220, April.
    10. Chunqiao Tan & Wenrui Feng & Weibin Han, 2020. "On the Banzhaf-like Value for Cooperative Games with Interval Payoffs," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    11. Boyang Dai & Xiangfeng Yang & Xiaoyue Liu, 2022. "Shapley Value of Uncertain Coalitional Game based on Hurwicz Criterion with Application to Water Resource Allocation," Group Decision and Negotiation, Springer, vol. 31(1), pages 241-260, February.
    12. ShinichiIshihara & Junnosuke Shino, 2023. "An AxiomaticAnalysisofIntervalShapleyValues," Working Papers 2214, Waseda University, Faculty of Political Science and Economics.
    13. Hsien-Chung Wu, 2018. "Interval-Valued Cores and Interval-Valued Dominance Cores of Cooperative Games Endowed with Interval-Valued Payoffs," Mathematics, MDPI, vol. 6(11), pages 1-26, November.
    14. 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.
    15. Yan-An Hwang & Wei-Yuan Yang, 2014. "A note on potential approach under interval games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 571-577, July.
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