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Theory and implementation of coalitional analysis in cooperative decision making

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  • Haiyan Xu

  • D. Kilgour

  • Keith Hipel

  • Edward McBean

Abstract

Stability definitions for describing human behavior under conflict when coalitions may form are generalized within the Graph Model for Conflict Resolution and algebraic formulations of these definitions are provided to allow computer implementation. The more general definitions of coalitional stabilities relax the assumption of transitive graphs capturing movements under the control of decision makers, either independently or cooperatively, and allow the convenient expansion to the case of coalitions of the four basic individual stabilities consisting of Nash stability, general metarationality, symmetric metarationality, and sequential stability. To permit the various coalitional stabilities to be efficiently calculated and conveniently encoded within a decision support system, algebraic expressions for the coalitional stabilities are provided in this research. Furthermore, a range of the theorems establish the mathematical credibility of employing the innovative algebraic approach to conflict resolution when coalitions are present. Finally, a conflict over the proposed exportation of bulk water from Lake Gisborne within the Canadian Province of Newfoundland and Labrador is modelled and analyzed to illustrate the practical application of the different coalitional stabilities and the strategic insights they provide. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:kap:theord:v:76:y:2014:i:2:p:147-171
    DOI: 10.1007/s11238-013-9363-6
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. 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.
    5. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
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    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. Shawei He, 2019. "Coalition Analysis in Basic Hierarchical Graph Model for Conflict Resolution with Application to Climate Change Governance Disputes," Group Decision and Negotiation, Springer, vol. 28(5), pages 879-906, October.
    3. Zhangpeng Tian & Fuxin Xu & Ruxin Nie, 2025. "Coalition Analysis Considering Decision Makers’ Psychological Behavior Characteristics and Full Participation of Sanctioning Opponents Within the Graph Model," Group Decision and Negotiation, Springer, vol. 34(5), pages 1145-1184, October.

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