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Matrix Representation of Conflict Resolution in Multiple-Decision-Maker Graph Models with Preference Uncertainty

Author

Listed:
  • Haiyan Xu

    (Nanjing University of Aeronautics and Astronautics)

  • D. Marc Kilgour

    (Wilfrid Laurier University)

  • Keith W. Hipel

    (University of Waterloo)

Abstract

Explicit matrix representations of solution concepts in a graph model of a multiple-decision-maker conflict with preference uncertainty are developed. In a graph model, the relative preferences of each DM over the available states are crucial in determining which states are stable according to any stability definition (solution concept). Unfortunately, it is often difficult to obtain accurate preference information in practical cases, so models that allow preference uncertainty can be very useful. In this work, stability definitions are extended to apply to graph models with this feature. The extension is easiest to implement using the matrix representation of a conflict model, which was developed to ease the coding of logically-defined stability definitions. Another benefit of matrix representation is that it facilitates modification and extension of the definitions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:grdene:v:20:y:2011:i:6:d:10.1007_s10726-010-9188-4
    DOI: 10.1007/s10726-010-9188-4
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    References listed on IDEAS

    as
    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. Steven J. Brams & Walter Mattli, 1993. "Theory of Moves: Overview and Examples," Conflict Management and Peace Science, Peace Science Society (International), vol. 12(2), pages 1-39, February.
    3. D. Marc Kilgour & Keith W. Hipel, 2005. "The Graph Model for Conflict Resolution: Past, Present, and Future," Group Decision and Negotiation, Springer, vol. 14(6), pages 441-460, November.
    4. Gregory W. Fischer & Mary Frances Luce & Jianmin Jia, 2000. "Attribute Conflict and Preference Uncertainty: Effects on Judgment Time and Error," Management Science, INFORMS, vol. 46(1), pages 88-103, January.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    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. Haiyan Xu & Yu Han & Ginger Y. Ke & Jun Zhu, 2022. "Modeling and Implementation of a New Negotiation Decision Support System for Conflict Resolution Under Uncertainty," Group Decision and Negotiation, Springer, vol. 31(3), pages 531-553, June.
    3. Leandro Chaves Rêgo & Giannini Italino Alves Vieira, 2020. "Alternative Generalized Metarationalities for Multiple Decision-Maker Conflicts," Group Decision and Negotiation, Springer, vol. 29(3), pages 461-490, June.
    4. 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.
    5. Giannini Italino Alves Vieira & Leandro Chaves Rêgo, 2020. "Berge Solution Concepts in the Graph Model for Conflict Resolution," Group Decision and Negotiation, Springer, vol. 29(1), pages 103-125, February.
    6. 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.
    7. 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.
    8. 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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