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Matrix representations of the inverse problem in the graph model for conflict resolution

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  • Wang, Junjie
  • Hipel, Keith W.
  • Fang, Liping
  • Dang, Yaoguo

Abstract

Given the final individual stability for each decision maker or an equilibrium of interest, a matrix-based method for an inverse analysis is developed in order to calculate all of the possible preferences for each decision maker creating the stability results based on the Nash, general metarationality, symmetric metarationality, or sequential stability definition of possible human interactions in a conflict. The matrix representations are furnished for the relative preferences, unilateral movements and improvements, as well as joint movements and joint improvements for a conflict having two or more decision makers. Theoretical conditions are derived for specifying required preference relationships in an inverse graph model. Under each of the four solution concepts, a matrix relationship is established to obtain all the available preferences for each decision maker causing the specific state to be an equilibrium. To explain how it can be employed in practice, this new approach to inverse analysis is applied to the Elsipogtog First Nation fracking dispute which took place in the Canadian Province of New Brunswick.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:1:p:282-293
    DOI: 10.1016/j.ejor.2018.03.007
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    References listed on IDEAS

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    1. Fang, Liping & Hipel, Keith W. & Kilgour, D. Marc, 1989. "Conflict models in graph form: Solution concepts and their interrelationships," European Journal of Operational Research, Elsevier, vol. 41(1), pages 86-100, July.
    2. O'Brien, Nicole L. & Hipel, Keith W., 2016. "A strategic analysis of the New Brunswick, Canada fracking controversy," Energy Economics, Elsevier, vol. 55(C), pages 69-78.
    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. 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.
    5. Steven J. Brams & Donald Wittman, 1981. "Nonmyopic Equilibria in 2×2 Games," Conflict Management and Peace Science, Peace Science Society (International), vol. 6(1), pages 39-62, September.
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    Citations

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    Cited by:

    1. 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.
    2. Qingye Han & Yuming Zhu & Ginger Y. Ke & Hongli Lin, 2019. "A Two-Stage Decision Framework for Resolving Brownfield Conflicts," IJERPH, MDPI, vol. 16(6), pages 1-19, March.
    3. 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.
    4. Yu Han & Haiyan Xu & Ginger Y. Ke, 2020. "Construction and application of hyper-inverse conflict models based on the sequential stability," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 237-259, November.
    5. Rêgo, Leandro Chaves & Silva, Hugo Victor & Rodrigues, Carlos Diego, 2021. "Optimizing the cost of preference manipulation in the graph model for conflict resolution," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    6. He, Shawei, 2022. "A time sensitive graph model for conflict resolution with application to international air carbon negotiation," European Journal of Operational Research, Elsevier, vol. 302(2), pages 652-670.
    7. 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.
    8. 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.
    9. Leandro Chaves Rêgo & Giannini Italino Alves Vieira, 2021. "Matrix Representation of Solution Concepts in the Graph Model for Conflict Resolution with Probabilistic Preferences and Multiple Decision Makers," Group Decision and Negotiation, Springer, vol. 30(3), pages 697-717, June.
    10. Keith W. Hipel & Liping Fang & D. Marc Kilgour, 2020. "The Graph Model for Conflict Resolution: Reflections on Three Decades of Development," Group Decision and Negotiation, Springer, vol. 29(1), pages 11-60, February.
    11. Yu Han & Haiyan Xu & Liping Fang & Keith W. Hipel, 2022. "An Integer Programming Approach to Solving the Inverse Graph Model for Conflict Resolution with Two Decision Makers," Group Decision and Negotiation, Springer, vol. 31(1), pages 23-48, February.

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