Advanced Search
MyIDEAS: Login to save this article or follow this journal

On the computation of the nucleolus of a cooperative game

Contents:

Author Info

  • Jeroen Kuipers

    ()
    (Department of Mathematics, Maastricht University, P.O.Box 616, 6200 MD Maastricht, The Netherlands. E-mail address: kuipers@math.unimaas.nl)

  • Ulrich Faigle

    ()
    (Zentrum für Angewandte Informatik, Universität zu Köln, Weyertal 80, 50931 Köln, Germany. E-mail address: faigle@zpr.uni-koeln.de)

  • Walter Kern

    ()
    (Department of Applied Mathematics, University of Twente, P.O.Box 217, 7500 AE Enschede, The Netherlands. E-mail address: kern@math.utwente.nl)

Abstract

We consider classes of cooperative games. We show that we can efficiently compute an allocation in the intersection of the prekernel and the least core of the game if we can efficiently compute the minimum excess for any given allocation. In the case where the prekernel of the game contains exactly one core vector, our algorithm computes the nucleolus of the game. This generalizes both a recent result by Kuipers on the computation of the nucleolus for convex games and a classical result by Megiddo on the nucleolus of standard tree games to classes of more general minimum cost spanning tree games. Our algorithm is based on the ellipsoid method and Maschler's scheme for approximating the prekernel.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://link.springer.de/link/service/journals/00182/papers/1030001/10300079.pdf
Download Restriction: Access to the full text of the articles in this series is restricted

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 30 (2001)
Issue (Month): 1 ()
Pages: 79-98

as in new window
Handle: RePEc:spr:jogath:v:30:y:2001:i:1:p:79-98

Note: Received February 2000/Final version April 2001
Contact details of provider:
Web page: http://link.springer.de/link/service/journals/00182/index.htm

Order Information:
Web: http://link.springer.de/orders.htm

Related research

Keywords:

References

No references listed on IDEAS
You can help add them by filling out this form.

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Guajardo, Mario & Jörnsten, Kurt, 2014. "Common Mistakes in Computing the Nucleolus," Discussion Papers 2014/15, Department of Business and Management Science, Norwegian School of Economics.
  2. Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
  3. Ulrich Faigle & Walter Kern & Jeroen Kuipers, 2006. "Computing an Element in the Lexicographic Kernel of a Game," Computational Statistics, Springer, vol. 63(3), pages 427-433, July.
  4. Kimms, Alf & Çetiner, Demet, 2012. "Approximate nucleolus-based revenue sharing in airline alliances," European Journal of Operational Research, Elsevier, vol. 220(2), pages 510-521.
  5. Cesco, Juan Carlos, 2008. "A general characterization for non-balanced games in terms of U-cycles," European Journal of Operational Research, Elsevier, vol. 191(2), pages 409-415, December.
  6. Granot, Daniel & Hamers, Herbert & Kuipers, Jeroen & Maschler, Michael, 2011. "On Chinese postman games where residents of each road pay the cost of their road," Games and Economic Behavior, Elsevier, vol. 72(2), pages 427-438, June.
  7. A. Palestini & G. Pignataro, 2013. "A multi-factor inequality approach to a transfer scheme: the case of Common Agricultural Policy," Working Papers wp891, Dipartimento Scienze Economiche, Universita' di Bologna.
  8. Péter Biró & Walter Kern & Daniël Paulusma, 2012. "Computing solutions for matching games," International Journal of Game Theory, Springer, vol. 41(1), pages 75-90, February.
  9. Kuipers, Jeroen & Mosquera, Manuel A. & Zarzuelo, José M., 2013. "Sharing costs in highways: A game theoretic approach," European Journal of Operational Research, Elsevier, vol. 228(1), pages 158-168.
  10. Takuya Masuzawa, 2008. "Computing the cores of strategic games with punishment–dominance relations," International Journal of Game Theory, Springer, vol. 37(2), pages 185-201, June.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:30:y:2001:i:1:p:79-98. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.