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Using matrices to link conflict evolution and resolution in a graph model

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  • Xu, Haiyan
  • Marc Kilgour, D.
  • Hipel, Keith W.
  • Kemkes, Graeme

Abstract

The graph model for conflict resolution provides a convenient and effective means to model and analyze a strategic conflict. Standard practice is to carry out a stability analysis of a graph model, and then to follow up with a post-stability analysis, an important component of which is status quo analysis. A graph model can be viewed as an edge-colored graph, but the fundamental problem of status quo analysis - to find a shortest colored path from the status quo node to a desired equilibrium - is different from the well-known network analysis problem of finding the shortest path between two nodes. The only matrix method that has been proposed cannot track all aspects of the evolution of a conflict from the status quo state. Our explicit algebraic approach is convenient for computer implementation and, as demonstrated with a real world case study, easy to use. It provides new insights into a graph model, not only identifying all equilibria reachable from the status quo, but also how to reach them. Moreover, this approach bridges the gap between stability analysis and status quo analysis in the graph model for conflict resolution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:1:p:318-329
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    References listed on IDEAS

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    1. K W Li & D M Kilgour & K W Hipel, 2005. "Status quo analysis in the graph model for conflict resolution," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 699-707, June.
    2. Ziliaskopoulos, Athanasios K. & Mandanas, Fotios D. & Mahmassani, Hani S., 2009. "An extension of labeling techniques for finding shortest path trees," European Journal of Operational Research, Elsevier, vol. 198(1), pages 63-72, October.
    3. 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.
    4. Barry, John & Proops, John, 1999. "Seeking sustainability discourses with Q methodology," Ecological Economics, Elsevier, vol. 28(3), pages 337-345, March.
    5. Davies, Cedric & Lingras, Pawan, 2003. "Genetic algorithms for rerouting shortest paths in dynamic and stochastic networks," European Journal of Operational Research, Elsevier, vol. 144(1), pages 27-38, January.
    6. Granat, Janusz & Guerriero, Francesca, 2003. "The interactive analysis of the multicriteria shortest path problem by the reference point method," European Journal of Operational Research, Elsevier, vol. 151(1), pages 103-118, November.
    7. 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. 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. 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.
    3. Shawei He & Keith Hipel & D. Kilgour, 2014. "Water Diversion Conflicts in China: A Hierarchical Perspective," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(7), pages 1823-1837, May.
    4. 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.
    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.

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