Advanced Search
MyIDEAS: Login to save this paper or follow this series

The restricted core of games on distributive lattices: how to share benefits in a hierarchy

Contents:

Author Info

  • Michel Grabisch

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Lijue Xie

    (China - chine)

Abstract

Finding a solution concept is one of the central problems in cooperative game theory, and the notion of core is the most popular solution concept since it is based on some rationality condition. In many real situations, not all possible coalitions can form, so that classical TU-games cannot be used. An interesting case is when possible coalitions are defined through a partial ordering of the players (or hierarchy). Then feasible coalitions correspond to teams of players, that is, one or several players with all their subordinates. In these situations, the core in its usual formulation may be unbounded, making its use difficult in practice. We propose a new notion of core, called the restricted core, which imposes efficiency of the allocation at each level of the hierarchy, is always bounded, and answers the problem of sharing benefits in a hierarchy. We show that the core we defined has properties very close to the classical case, with respect to marginal vectors, the Weber set, and balancedness.

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://halshs.archives-ouvertes.fr/docs/00/58/38/68/PDF/mmor09-2.pdf
Download Restriction: no

Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00583868.

as in new window
Length:
Date of creation: 2011
Date of revision:
Publication status: Published, Mathematical Methods of Operations Research, 2011, 73, 2, 189-208
Handle: RePEc:hal:cesptp:halshs-00583868

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00583868
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/

Related research

Keywords: cooperative game; feasible coalition; core; hierarchy;

Other versions of this item:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Michel Grabisch & Fabien Lange, 2007. "Games on lattices, multichoice games and the Shapley value: a new approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00178916, HAL.
  2. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, Springer, vol. 21(3), pages 249-66.
  3. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2007. "Distributing Dividends in Games with Ordered Players," Tinbergen Institute Discussion Papers, Tinbergen Institute 06-114/1, Tinbergen Institute.
  4. Ambec, S. & Sprumont, Y., 2000. "Sharing a River," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 2000-08, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. repec:hal:journl:halshs-00178916 is not listed on IDEAS
  6. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," PSE - Labex "OSE-Ouvrir la Science Economique", HAL hal-00803233, HAL.
  7. Hans Reijnierse & Jean Derks, 1998. "Note On the core of a collection of coalitions," International Journal of Game Theory, Springer, Springer, vol. 27(3), pages 451-459.
  8. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, Elsevier, vol. 25(2), pages 283-286, October.
  9. Michel Grabisch & Lijue Xie, 2007. "A new approach to the core and Weber set of multichoice games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00267933, HAL.
  10. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, Springer, vol. 20(3), pages 277-93.
  11. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 112(4), pages 754-778, August.
  12. Bilbao, J. M. & Lebron, E. & Jimenez, N., 1999. "The core of games on convex geometries," European Journal of Operational Research, Elsevier, Elsevier, vol. 119(2), pages 365-372, December.
  13. Michel Grabisch & Lijue Xie, 2008. "The core of games on distributive lattices : how to share benefits in a hierarchy," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne b08077, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Sep 2009.
  14. repec:hal:journl:halshs-00445171 is not listed on IDEAS
  15. Algaba, A. & Bilbao, J.M. & Brink, J.R. van den & Jiménez-Losada, A., 2000. "Cooperative Games on Antimatroids," Discussion Paper, Tilburg University, Center for Economic Research 2000-124, Tilburg University, Center for Economic Research.
  16. Derks, Jean J M & Gilles, Robert P, 1995. "Hierarchical Organization Structures and Constraints on Coalition Formation," International Journal of Game Theory, Springer, Springer, vol. 24(2), pages 147-63.
  17. René Brink & Gerard Laan & Valeri Vasil’ev, 2007. "Component efficient solutions in line-graph games with applications," Economic Theory, Springer, Springer, vol. 33(2), pages 349-364, November.
  18. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, Elsevier, vol. 5(2), pages 240-256, April.
  19. repec:hal:journl:halshs-00267933 is not listed on IDEAS
Full references (including those not matched with items on IDEAS)

Citations

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

Cited by:
  1. Michel Grabisch & Peter Sudhölter, 2014. "On the restricted cores and the bounded core of games on distributive lattices," PSE - Labex "OSE-Ouvrir la Science Economique", HAL halshs-00950109, HAL.
  2. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," PSE - Labex "OSE-Ouvrir la Science Economique", HAL hal-00803233, HAL.

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:hal:cesptp:halshs-00583868. 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: (CCSD).

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.