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A Basic Hierarchical Graph Model for Conflict Resolution with Weighted Preference

S. He1, D. M. Kilgour2,3, and K. W. Hipel3,4,5*

  1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106,China
  2. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada
  3. Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  4. Centre for International Governance Innovation, Waterloo, Ontario N2L 6C2, Canada
  5. Balsillie School of International Affairs, Waterloo, Ontario, N2L 6C2, Canada

*Corresponding author. Tel.: +(1) 519 888-4567; fax: +(1) 519 746-4791. E-mail address: (K.W. Hipel).


A novel hierarchical graph model for conflict resolution in which preferences are determined by weighting component graphs is proposed. This weighted hierarchical model contains three decision makers (DMs), one common decision maker (CDM) appearing in two local graphs, each with one local decision maker. Reachable lists and unilateral improvements for DMs are represented by matrices, which can be used to calculate stability results. Theorems reveal the relationship between the stability results in the hierarchical graph and in each local graph. Algorithms are designed to capitalize on these relationships in the calculation of stability. A case study of water diversion conflicts in China is provided to show how the new methodology can be applied in practice. The weighted hierarchical graph model improves the modeling of hierarchical conflicts by providing more flexibility in describing the preference of the CDM, who is the key decision-maker.

Keywords: hierarchical graph model, graph model for conflict resolution (GMCR), matrix representation, stability definitions, water diversion conflicts

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