Skip to main content
SpringerLink
Log in

Matrix Representation of a Basic Hierarchical Graph Model for Conflict Resolution

  • Conference paper
  • First Online:
Decision Support Systems IV – Information and Knowledge Management in Decision Processes (EWG-DSS 2014, EWG-DSS 2014)

Part of the book series: Lecture Notes in Business Information Processing ((LNBIP,volume 221))

Abstract

A basic hierarchical graph model for conflict resolution is proposed to handle a hierarchical conflict with two smaller conflicts as components. The hierarchical model can be represented in matrices and its stabilities calculated. This novel methodology is applied to water diversion conflicts in China, where the two subconflicts are caused by the construction of two local subprojects. Strategic analysis can provide decision makers (DMs) with a comprehensive understanding of a conflict and guidance for action. For basic hierarchical graph model, the matrix approach is an effective and convenient way to represent the model, calculate stability results, and predict equilibria.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 44.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Li, K.W., Kilgour, D.M., Hipel, K.W.: Status quo analysis in the graph model for conflict resolution. J. Oper. Res. Soc. 56(6), 699–707 (2005)

    Article  Google Scholar 

  2. Kilgour, D.M., Hipel, K.W.: The graph model for conflict resolution: past, present, and future. Group Decis. Negot. 14(6), 441–460 (2005)

    Article  Google Scholar 

  3. Kilgour, D.M., Hipel, K.W.: Conflict analysis methods: the graph model for conflict resolution. In: Kilgou, D.M., Eden, C. (eds.) Handbook of Group Decision and Negotiation. Advances in Group Decision and Negotiation, p. 203. Springer, The Netherlands (2010)

    Chapter  Google Scholar 

  4. Von Neumann, J., Morgenstern, O.B.: Theory of games and economic behavior, 1st edn. Princeton University Press, Princeton (1944)

    MATH  Google Scholar 

  5. Howard, N.: Paradoxes of Rationality: Theory of Metagames and Political Behavior. MIT Press, Cambridge (1971)

    Google Scholar 

  6. Howard, N.: Confrontation analysis: how to win operations other than war, Technical report, C4ISR (1999)

    Google Scholar 

  7. Nash, J.F.: Equilibrium points in n-person games. In: Proceedings of the national academy of sciences 36(1), 48–49 (1950)

    Google Scholar 

  8. Nash, J.F.: Non-cooperative games. Annals Math. 54(2), 286–295 (1951)

    Article  MathSciNet  Google Scholar 

  9. Fraser, N.M., Hipel, K.W.: Conflict Analysis: Models and Resolutions. North-Holland (1984)

    Google Scholar 

  10. Kilgour, D.M., Hipel, K.W., Fang, L., Peng, X.J.: Coalition analysis in group decision support. Group Decis. Negot. 10(2), 159–175 (2001)

    Article  Google Scholar 

  11. Inohara, T., Hipel, K.W.: Coalition analysis in the graph model for conflict resolution. Syst. Eng. 11(4), 343–359 (2008)

    Article  Google Scholar 

  12. Inohara, T., Hipel, K.W.: Interrelationships among noncooperative and coalition stability concepts. J. Syst. Sci. Syst. Eng. 17(1), 1–9 (2008)

    Article  Google Scholar 

  13. Hamouda, L., Kilgour, D.M., Hipel, K.W.: Strength of preference in the graph model for conflict resolution. Group Decis. Negot. 13(5), 449–462 (2004)

    Article  Google Scholar 

  14. Xu, H., Kilgour, D.M., Hipel, K.W.: Matrix representation and extension of coalition analysis in group decision support. Comput. Math. Appl. 60(5), 1164–1176 (2010)

    Article  MathSciNet  Google Scholar 

  15. Xu, H., Kilgour, D.M., Hipel, K.W., Kemkes, G.: Using matrices to link conflict evolution and resolution in a graph model. Eur. J. Oper. Res. 207(1), 318–329 (2010)

    Article  MathSciNet  Google Scholar 

  16. He, S., Hipel, K.W., Kilgour, D.M.: Water diversion conflicts in China: a hierarchical perspective. Water Resour. Manage 28, 1823–1837 (2014)

    Article  Google Scholar 

  17. Chen, Z., Wang, H., Qi, X.: Pricing and water resource allocation scheme for the south-to-north water diversion project in China. Water Resour. Manage 27(5), 1457–1472 (2013)

    Article  Google Scholar 

  18. Yang, H., Zehnder, A.J.: The south-north water transfer project in China: an analysis of water demand uncertainty and environmental objectives in decision making. Water Int. 30(3), 339–349 (2005)

    Article  Google Scholar 

  19. Berkoff, J.: China: the South-North water transfer project-is it justified? Water Policy 5(1), 1–28 (2003)

    Article  Google Scholar 

  20. He, S., Kilgour, D.M., Hipel, K.M.: A basic hierarchical graph model for conflict resolution with application to water diversion conflicts in China. INFOR: Inf. Syst. Oper. Res. 51(3), 103–119 (2013)

    MathSciNet  Google Scholar 

  21. Xu, H., Hipel, K.W., Kilgour, D.M.: Matrix representation of conflicts with two decision-makers. In: Procedings IEEE Inernational Conference System Man Cybern., vol. 1, pp. 1764–1769 (2007)

    Google Scholar 

  22. Xu, H., Hipel, K.W., Kilgour, D.M.: Matrix representation of solution concepts in multiple-decision-maker graph models. IEEE Trans. Syst. Man Cybern. 39(1), 96–108 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Shawei He, D. Marc Kilgour & Keith W. Hipel

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

    D. Marc Kilgour

  3. Centre for International Governance Innovation, Waterloo, ON, N2L 6C2, Canada

    Keith W. Hipel

  4. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Qinhuai District, Nanjing, 210016, China

    Shawei He

Authors
  1. Shawei He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Marc Kilgour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Keith W. Hipel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Marc Kilgour .

Editor information

Editors and Affiliations

  1. University of Namur, Namur, Belgium

    Isabelle Linden

  2. University of Plymouth, Plymouth, UK

    Shaofeng Liu

  3. SimTech Simulation Technology, Graz, Austria

    Fátima Dargam

  4. University of Liverpool, Liverpool, UK

    Jorge E. Hernández

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

He, S., Kilgour, D.M., Hipel, K.W. (2015). Matrix Representation of a Basic Hierarchical Graph Model for Conflict Resolution. In: Linden, I., Liu, S., Dargam, F., Hernández, J.E. (eds) Decision Support Systems IV – Information and Knowledge Management in Decision Processes. EWG-DSS EWG-DSS 2014 2014. Lecture Notes in Business Information Processing, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-21536-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21536-5_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21535-8

  • Online ISBN: 978-3-319-21536-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation