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Theory and implementation of coalitional analysis in cooperative decision making

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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.

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Acknowledgments

The author, Haiyan Xu, is thankful for the financial support from the National Natural Science Foundation of China (NSFC) (71071076) and National Social Science Foundation of China (12AZD102). The authors would also like to thank the National Science and Engineering Research Council (NSERC) of Canada for financial support.

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Authors and Affiliations

  1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China

    Haiyan Xu

  2. College of Physical and Engineering Science, University of Guelph, Guelph, ON, Canada

    Haiyan Xu & Edward A. McBean

  3. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, Canada

    D. Marc Kilgour

  4. Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Keith W. Hipel

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  1. Haiyan Xu
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  2. D. Marc Kilgour
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  3. Keith W. Hipel
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  4. Edward A. McBean
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Correspondence to Keith W. Hipel.

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Xu, H., Kilgour, D.M., Hipel, K.W. et al. Theory and implementation of coalitional analysis in cooperative decision making. Theory Decis 76, 147–171 (2014). https://doi.org/10.1007/s11238-013-9363-6

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