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Group Decision and Negotiation

, Volume 20, Issue 6, pp 755–779 | Cite as

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

  • Haiyan Xu
  • D. Marc Kilgour
  • Keith W. Hipel
Article

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.

Keywords

Matrix representation Solution concepts Graph model Preference uncertainty Decision makers 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.College of Economics and ManagementNanjing University of Aeronautics and AstronauticsNanjing, JiangsuChina
  2. 2.Department of MathematicsWilfrid Laurier UniversityWaterlooCanada
  3. 3.Department of Systems Design EngineeringUniversity of WaterlooWaterlooCanada

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