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Mixed stabilities for analyzing opponents’ heterogeneous behavior within the graph model for conflict resolution

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  • Zhao, Shinan
  • Xu, Haiyan
  • Hipel, Keith W.
  • Fang, Liping

Abstract

Mixed stabilities are incorporated into the Graph Model for Conflict Resolution (GMCR) for modeling and analyzing a complicated conflict with heterogeneous opponents, consisting of both credible and non-credible players. To identify the mixed coalitional movements, mixed unilateral improvements (MUIs) are constructed in this research followed by a specific example. Subsequently, two types of mixed stabilities are developed within the GMCR paradigm for conveniently portraying different sanctioning behavior of heterogeneous opponents. Compared to general metarationality (GMR), symmetric metarationality (SMR) and sequential stability (SEQ), mixed stabilities take into account different sanctioning moves by opponents, which is more practical and useful for investigating real-world disputes. Furthermore, the interrelationships among mixed stabilities and four classical stabilities are discussed. Subsequently, equilibria with mixed stabilities are proposed, in which each decision maker may adopt a different solution concept defining his or her behavior. To enhance the efficiency of mixed stability calculations, the algebraic representations of mixed stabilities are then constructed. Finally, a generic environmental conflict in China is utilized to demonstrate how mixed stabilities can be employed to effectively address an actual dispute with heterogeneous opponents.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:277:y:2019:i:2:p:621-632
    DOI: 10.1016/j.ejor.2019.02.043
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    References listed on IDEAS

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    1. Luai Hamouda & D. Marc Kilgour & Keith W. Hipel, 2004. "Strength of Preference in the Graph Model for Conflict Resolution," Group Decision and Negotiation, Springer, vol. 13(5), pages 449-462, September.
    2. Xu, Haiyan & Marc Kilgour, D. & Hipel, Keith W. & Kemkes, Graeme, 2010. "Using matrices to link conflict evolution and resolution in a graph model," European Journal of Operational Research, Elsevier, vol. 207(1), pages 318-329, November.
    3. Amer Obeidi & D. Marc Kilgour & Keith W. Hipel, 2009. "Perceptual Graph Model Systems," Group Decision and Negotiation, Springer, vol. 18(3), pages 261-277, May.
    4. 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.
    5. Haiyan Xu & D. Kilgour & Keith Hipel & Edward McBean, 2014. "Theory and implementation of coalitional analysis in cooperative decision making," Theory and Decision, Springer, vol. 76(2), pages 147-171, February.
    6. 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.
    7. 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.
    8. M. Abul Bashar & Keith W. Hipel & D. Marc Kilgour & Amer Obeidi, 2018. "Interval fuzzy preferences in the graph model for conflict resolution," Fuzzy Optimization and Decision Making, Springer, vol. 17(3), pages 287-315, September.
    9. Haiyan Xu & D. Marc Kilgour & Keith W. Hipel, 2011. "Matrix Representation of Conflict Resolution in Multiple-Decision-Maker Graph Models with Preference Uncertainty," Group Decision and Negotiation, Springer, vol. 20(6), pages 755-779, November.
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    Citations

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    Cited by:

    1. Shinan Zhao & Haiyan Xu, 2019. "A Novel Preference Elicitation Technique Based on a Graph Model and Its Application to a Brownfield Redevelopment Conflict in China," IJERPH, MDPI, vol. 16(21), pages 1-14, October.
    2. Liangyan Tao & Xuebi Su & Saad Ahmed Javed, 2021. "Inverse Preference Optimization in the Graph Model for Conflict Resolution based on the Genetic Algorithm," Group Decision and Negotiation, Springer, vol. 30(5), pages 1085-1112, October.
    3. Rêgo, Leandro Chaves & Kilgour, D. Marc, 2022. "Choice stabilities in the graph model for conflict resolution," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1064-1071.
    4. 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.
    5. 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.
    6. Huang, Yuming & Ge, Bingfeng & Hipel, Keith W. & Fang, Liping & Zhao, Bin & Yang, Kewei, 2023. "Solving the inverse graph model for conflict resolution using a hybrid metaheuristic algorithm," European Journal of Operational Research, Elsevier, vol. 305(2), pages 806-819.
    7. Ming Tang & Huchang Liao, 2022. "A graph model for conflict resolution with inconsistent preferences among large-scale participants," Fuzzy Optimization and Decision Making, Springer, vol. 21(3), pages 455-478, September.

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