Skip to main content

Supporting Cooperative Decisions with a Multicriteria Generalization of the Nash Solution

  • Conference paper
  • First Online:
Computational Collective Intelligence

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9330))

Abstract

A decision situation is considered in which two decision makers negotiate cooperation conditions to realize a joint project. Each decision maker has his own set of criteria measuring results of the cooperation. The situation is modeled as the multicriteria bargaining problem. A special multiround mediation procedure is presented which can be implemented in a computer-based system. According to the procedure the system supports multicriteria analysis made by the decision makers and generates mediation proposals. The mediation proposals are derived on the basis of the original solution to the multicriteria problem, presented in the paper. The solution expresses preferences of the decision makers. It generalizes the classic Nash solution concept on the multicriteria case.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fisher, R., Ury, W.: Getting to Yes. Hougton Mifflin, Boston (1981)

    Google Scholar 

  2. Imai, H.: Individual Monotonicity and Lexicographical Maxmin Solution. Econometrica 51, 389–401 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kalai, E., Smorodinsky, M.: Other Solutions to Nash’s Bargaining Problem. Econometrica 43, 513–518 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kruś, L.: Computer-based support in multicriteria bargaining with the use of the generalized raiffa solution concept. In: Angelov, P., et al. (eds.) Intelligent Systems 2014. AISC, vol. 322, pp. 117–128. Springer, Heidelberg (2015)

    Google Scholar 

  5. Kruś, L.: Multicriteria cooperative decisions, methods of computer-based support (in Polish: wielokryterialne decyzje kooperacyjne, metody wspomagania komput- erowego). Badania systemowe, vol. 70, p. 248 Warsaw, Systems Research Institute, Polish Academy of Sciences (2011)

    Google Scholar 

  6. Kruś, L.: Multicriteria decision support in bargaining, a problem of players’s manipulations. In: Trzaskalik, T., Michnik, J. (eds.) Multiple Objective and Goal Programming Recent Developments, pp. 143–160. Physica verlag, Heidelberg (2001)

    Google Scholar 

  7. Kruś, L.: Multicriteria Decision Support in Negotiations. Control and Cybernetics 25(6), 1245–1260 (1996)

    MathSciNet  MATH  Google Scholar 

  8. Kruś, L., Bronisz, P.: Some new results in interactive approach to multicriteria bargaining. In: Wierzbicki, A.P., et al. (eds.) User Oriented Methodology and Techniques of Decision Analysis. Lecture Notes in Economics and Mathematical Systems, vol. 397, pp. 21–34. Springer, Berlin (1993)

    Chapter  Google Scholar 

  9. Moulin, H.: Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge (1988)

    Book  MATH  Google Scholar 

  10. Nash, J.F.: The Bargaining Problem. Econometrica 18, 155–162 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  11. Nash, J.F.: Two-Person Cooperative Games. Econometrica 21, 129–140 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  12. Peters, H.: Bargaining Game Theory. Ph.D. Thesis, Catholic University of Nijmegen, The Nederlands (1986)

    Google Scholar 

  13. Raiffa, H.: Arbitration Schemes for Generalized Two-Person Games. Annals of Mathematics Studies (28), 361–387. Princeton (1953)

    Google Scholar 

  14. Raiffa, H.: The Art and Science of Negotiations. Harvard Univ. Press, Cambridge (1982)

    Google Scholar 

  15. Roth, A.E.: Axiomatic Model of Bargaining. Lecture Notes in Economics and Mathematical Systems, vol. 170. Springer, Berlin (1979)

    Book  MATH  Google Scholar 

  16. Thomson, W.: Two Characterization of the Raiffa Solution. Economic Letters 6, 225–231 (1980)

    Article  MathSciNet  Google Scholar 

  17. Wierzbicki, A.P.: On the Completeness and Constructiveness of Parametric Characterizations to Vector Optimization Problems. OR Spectrum 8, 73–87 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wierzbicki, A.P., Makowski, M., Wessels, J.: Model-based Decision Support Methodology with Environmental Applications. Kluwer Academic Press, Dordrecht (2000)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lech Kruś .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kruś, L. (2015). Supporting Cooperative Decisions with a Multicriteria Generalization of the Nash Solution. In: Núñez, M., Nguyen, N., Camacho, D., Trawiński, B. (eds) Computational Collective Intelligence. Lecture Notes in Computer Science(), vol 9330. Springer, Cham. https://doi.org/10.1007/978-3-319-24306-1_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24306-1_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24305-4

  • Online ISBN: 978-3-319-24306-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics