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An Integer Programming Approach to Solving the Inverse Graph Model for Conflict Resolution with Two Decision Makers

Author

Listed:
  • Yu Han

    (Nanjing University of Aeronautics and Astronautics)

  • Haiyan Xu

    (Nanjing University of Aeronautics and Astronautics)

  • Liping Fang

    (Ryerson University)

  • Keith W. Hipel

    (University of Waterloo
    Balsillie School of International Affairs
    Centre for International Governance Innovation)

Abstract

Operational algorithms for solving the inverse problem for the graph model for conflict resolution are presented for the case of two decision makers (DMs) under a variety of solution concepts, including Nash stability (Nash), general metarationality (GMR), symmetric metarationality (SMR), and sequential stability (SEQ). The algorithms based on integer programming enable a DM, an analyst, or a mediator to obtain all of the preferences required to make a specified state to be an equilibrium or resolution. For the cases of Nash, GMR, and SMR, the respective inverse algorithm for the focal DM is formulated as a 0–1 integer linear programming problem even when both DMs’ preferences are unknown. For the situation of SEQ, when both DMs’ preferences are unknown, the focal DM’s algorithm is a 0–1 integer nonlinear programming problem while, under the condition that the opponent’s preferences are known, the focal DM’s 0–1 integer programming problem is linear. The usefulness of the algorithms developed is demonstrated by applying them to an illustrative dispute.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:grdene:v:31:y:2022:i:1:d:10.1007_s10726-021-09755-w
    DOI: 10.1007/s10726-021-09755-w
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    References listed on IDEAS

    as
    1. Garcia, A. & Hipel, K.W., 2017. "Inverse engineering preferences in simple games," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 184-194.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
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    Citations

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    Cited by:

    1. Xiufen Gu & Lailei Gu & Dayong Wang & Sajad Jamshidi, 2023. "Resolving Trans-Boundary Water Conflicts: Third-Party Mediation Using an Inverse Approach of GMCR Under Incomplete Preference Environments," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(15), pages 6071-6088, December.
    2. 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.
    3. Zhu, Ziming & Kilgour, D. Marc & Hipel, Keith W. & Yu, Jing, 2025. "Interrelationships of Non-cooperative, Classical and Pareto coalitional stability definitions," European Journal of Operational Research, Elsevier, vol. 321(3), pages 884-894.
    4. Zhu, Yan & Dong, Yucheng & Zhang, Hengjie & Fang, Liping, 2025. "Exploring the minimum cost conflict mediation path to a desired resolution within the inverse graph model framework," European Journal of Operational Research, Elsevier, vol. 321(2), pages 543-564.

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