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The potential and consistency of the Owen value for fuzzy cooperative games with a coalition structure

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Listed:
  • Zijun Li

    (Central South University)

  • Fanyong Meng

    (Central South University)

Abstract

This paper extends the potential function and consistency to the Owen value for fuzzy cooperative games with a coalition structure. First, we prove that the unique payoff index satisfying the potential function is the Owen value. Then, we characterize the Owen value for fuzzy cooperative games with a coalition structure by fuzzy balanced contributions and fuzzy consistency, respectively. Finally, an example in supply chain is given to illustrate the relationship between the Owen value and potential function for fuzzy cooperative games with a coalition structure and solve the problem of payoff distribution in supply chain under fuzzy environment.

Suggested Citation

  • Zijun Li & Fanyong Meng, 2023. "The potential and consistency of the Owen value for fuzzy cooperative games with a coalition structure," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 387-414, September.
    • Handle: RePEc:spr:fuzodm:v:22:y:2023:i:3:d:10.1007_s10700-022-09397-w
    DOI: 10.1007/s10700-022-09397-w
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    References listed on IDEAS

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    1. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 129(3), pages 596-618, March.
    2. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Dragan, Irinel, 1996. "New mathematical properties of the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 95(2), pages 451-463, December.
    4. Butnariu, Dan & Kroupa, Tomas, 2008. "Shapley mappings and the cumulative value for n-person games with fuzzy coalitions," European Journal of Operational Research, Elsevier, vol. 186(1), pages 288-299, April.
    5. Huang, Wei & Swaminathan, Jayashankar M., 2009. "Introduction of a second channel: Implications for pricing and profits," European Journal of Operational Research, Elsevier, vol. 194(1), pages 258-279, April.
    6. Winter, Eyal, 1992. "The consistency and potential for values of games with coalition structure," Games and Economic Behavior, Elsevier, vol. 4(1), pages 132-144, January.
    7. Tijs, S.H. & Brânzei, R. & Ishihara, S. & Muto, S., 2004. "On cores and stable sets for fuzzy games," Other publications TiSEM 66dd20be-cb4b-4b6d-937e-0, Tilburg University, School of Economics and Management.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    9. Yi Zhang & Jinwu Gao & Xiang Li & Xiangfeng Yang, 2021. "Two-person cooperative uncertain differential game with transferable payoffs," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 567-594, December.
    10. Rong Zou & Genjiu Xu & Wenzhong Li & Xunfeng Hu, 2020. "A coalitional compromised solution for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 735-758, December.
    11. Pei Liang & Junhua Hu & Bo Li & Yongmei Liu & Xiaohong Chen, 2020. "A group decision making with probability linguistic preference relations based on nonlinear optimization model and fuzzy cooperative games," Fuzzy Optimization and Decision Making, Springer, vol. 19(4), pages 499-528, December.
    12. 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.
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