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A characterization of the Owen value via sign symmetries

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Listed:
  • Xinjuan Chen

    (Guangzhou Xinhua University Institute of Fortune Management Research (IFMR))

  • Minghua Zhan

    (Guangdong University of Foreign Studies Institute of Fortune Management Research (IFMR))

  • Zhihui Zhao

    (Zhejiang Sci-Tech University)

Abstract

Khmelnitskaya and Yanovskaya (Math Methods Oper Res 66(2):255–261, 2007) characterized the Owen value for TU games with a coalition structure by the axioms of efficiency, marginality, symmetry across coalitions and symmetry within coalitions. Symmetry across components requires that components with equally productive in the game between components obtain the same total payoffs of their members. In this note, inspired by Casajus (Econ Lett 169:59–62, 2018), we weaken the symmetry across components to the sign symmetry across components, which requires only that equally productive components obtain the same sign of total payoffs. We extend the Khmelnitskaya-Yanovskaya’s characterization by using efficiency, marginality, sign symmetry across coalitions, and sign symmetry within coalitions, similarly as it was done by Casajus (Econ Lett 169:59–62, 2018) for the Shapley value for general TU games. At last, we extend the main result to the Winter value for games with level structure

Suggested Citation

  • Xinjuan Chen & Minghua Zhan & Zhihui Zhao, 2024. "A characterization of the Owen value via sign symmetries," Theory and Decision, Springer, vol. 97(3), pages 553-561, November.
    • Handle: RePEc:kap:theord:v:97:y:2024:i:3:d:10.1007_s11238-024-09985-9
    DOI: 10.1007/s11238-024-09985-9
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    References listed on IDEAS

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    1. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 227-240.
    2. Casajus, André & Yokote, Koji, 2017. "Weak differential marginality and the Shapley value," Journal of Economic Theory, Elsevier, vol. 167(C), pages 274-284.
    3. Xun-Feng Hu, 2021. "New axiomatizations of the Owen value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 585-603, June.
    4. André Casajus & Rodrigue Tido Takeng, 2023. "Second-order productivity, second-order payoffs, and the Owen value," Annals of Operations Research, Springer, vol. 320(1), pages 1-13, January.
    5. André Casajus, 2010. "Another characterization of the Owen value without the additivity axiom," Theory and Decision, Springer, vol. 69(4), pages 523-536, October.
    6. Albizuri, M.J., 2008. "Axiomatizations of the Owen value without efficiency," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 78-89, January.
    7. Anna Khmelnitskaya & Elena Yanovskaya, 2007. "Owen coalitional value without additivity axiom," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 255-261, October.
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