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The graph model for composite decision makers and its application to a water resource conflict

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  • Wu, Nannan
  • Xu, Yejun
  • Kilgour, D. Marc
  • Fang, Liping

Abstract

To analyze a strategic conflict involving composite decision makers (CDMs), this paper uses the methodology of the Graph Model for Conflict Resolution (GMCR). A CDM is a group of individuals with differing decision characteristics – conservative or aggressive – any one of whom can make a decision on behalf of the group. In our model, a conservative CDM makes moves that take into account the interests of all group members, aiming to protect each one from possible sanctions; an aggressive CDM gives priority to some individuals that will benefit and does not necessarily consider the interests of other group members when making moves. Based on these different decision characteristics, two versions of hesitant fuzzy stability definitions, indexed I and II, are proposed. To facilitate the stability analysis of the graph model with multiple decision makers (DMs), including at least one CDM, a matrix-based method called Matrix Representation for Hesitant Fuzzy Stability is developed to identify the equilibria of the model, or states that are stable for all DMs and are therefore possible resolutions of the conflict. A water resource conflict in the Lancang-Mekong River basin is utilized to demonstrate the system. The results reveal how the decision characteristics of CDMs can influence the equilibria of a conflict.

Suggested Citation

  • Wu, Nannan & Xu, Yejun & Kilgour, D. Marc & Fang, Liping, 2023. "The graph model for composite decision makers and its application to a water resource conflict," European Journal of Operational Research, Elsevier, vol. 306(1), pages 308-321.
    • Handle: RePEc:eee:ejores:v:306:y:2023:i:1:p:308-321
    DOI: 10.1016/j.ejor.2022.07.046
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    References listed on IDEAS

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    1. Wang, Junjie & Hipel, Keith W. & Fang, Liping & Dang, Yaoguo, 2018. "Matrix representations of the inverse problem in the graph model for conflict resolution," European Journal of Operational Research, Elsevier, vol. 270(1), pages 282-293.
    2. Zhao, Shinan & Xu, Haiyan & Hipel, Keith W. & Fang, Liping, 2019. "Mixed stabilities for analyzing opponents’ heterogeneous behavior within the graph model for conflict resolution," European Journal of Operational Research, Elsevier, vol. 277(2), pages 621-632.
    3. He, Shawei & Marc Kilgour, D. & Hipel, Keith W., 2017. "A general hierarchical graph model for conflict resolution with application to greenhouse gas emission disputes between USA and China," European Journal of Operational Research, Elsevier, vol. 257(3), pages 919-932.
    4. Kevin W. Li & Keith W. Hipel & D. Marc Kilgour & Donald Noakes, 2005. "Integrating Uncertain Preferences into Status Quo Analysis with Applications to an Environmental Conflict," Group Decision and Negotiation, Springer, vol. 14(6), pages 461-479, November.
    5. Haiyan Xu & Keith Hipel & D. Kilgour & Ye Chen, 2010. "Combining strength and uncertainty for preferences in the graph model for conflict resolution with multiple decision makers," Theory and Decision, Springer, vol. 69(4), pages 497-521, October.
    6. D. Marc Kilgour & Keith W. Hipel & Liping Fang & Xiaoyong (John) Peng, 2001. "Coalition Analysis in Group Decision Support," Group Decision and Negotiation, Springer, vol. 10(2), pages 159-175, March.
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    Cited by:

    1. Sabino, Emerson Rodrigues & Rêgo, Leandro Chaves, 2024. "Minimax regret stability in the graph model for conflict resolution," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1087-1097.

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