IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper

The core of games on ordered structures and graphs

  • Michel Grabisch

    ()

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In many situations, this assumption is too strong and one has to deal with some unfeasible coalitions. Defining a game on a subcollection of the power set of the set of players has many implications on the mathematical structure of the core, depending on the precise structure of the subcollection of feasible coalitions. Many authors have contributed to this topic, and we give a unified view of these different results.

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: https://halshs.archives-ouvertes.fr/halshs-00445171/document
Download Restriction: no

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00445171.

as
in new window

Length:
Date of creation: Oct 2009
Date of revision:
Publication status: Published in 4OR: A Quarterly Journal of Operations Research, Springer Verlag, 2009, 7 (3), pp.207-238. <10.1007/s10288-009-0109-9>
Handle: RePEc:hal:cesptp:halshs-00445171
DOI: 10.1007/s10288-009-0109-9
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00445171
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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. Gilboa, Itzhak & Lehrer, Ehud, 1991. "Global Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 129-47.
  2. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-66.
  3. Michel Grabisch & Lijue Xie, 2011. "The restricted core of games on distributive lattices: how to share benefits in a hierarchy," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 189-208, April.
  4. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2008. "The average tree solution for cycle-free graph games," Other publications TiSEM f243609c-2847-415f-ae52-1, Tilburg University, School of Economics and Management.
  5. Michel Grabisch, 2009. "The core of games on ordered structures and graphs," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445171, HAL.
  6. repec:hal:journl:halshs-00583868 is not listed on IDEAS
  7. repec:spr:compst:v:73:y:2011:i:2:p:189-208 is not listed on IDEAS
  8. Faigle, U. & Grabisch, M. & Heyne, M., 2010. "Monge extensions of cooperation and communication structures," European Journal of Operational Research, Elsevier, vol. 206(1), pages 104-110, October.
  9. Derks, Jean & Peters, Hans, 1998. "Orderings, excess functions, and the nucleolus," Mathematical Social Sciences, Elsevier, vol. 36(2), pages 175-182, September.
  10. Jean Derks & Gerard Laan & Valery Vasil’ev, 2010. "On the Harsanyi payoff vectors and Harsanyi imputations," Theory and Decision, Springer, vol. 68(3), pages 301-310, March.
  11. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00650964, HAL.
  12. René Brink & Gerard Laan & Valeri Vasil’ev, 2007. "Component efficient solutions in line-graph games with applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 349-364, November.
  13. Gilles, R.P. & Owen, G. & van den Brink, J.R., 1991. "Games with permission structures : The conjunctive approach," Research Memorandum FEW 473, Tilburg University, School of Economics and Management.
  14. Gabrielle Demange, 1994. "Intermediate Preferences and Stable Coalition Structures," Post-Print halshs-00670920, HAL.
  15. Alain Chateauneuf & Jean-Yves Jaffray, 2008. "Some Characterizations of Lower Probabilities and Other Monotone Capacities through the Use of Mobius Inversion," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00649208, HAL.
  16. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Rooted-tree solutions for tree games," European Journal of Operational Research, Elsevier, vol. 203(2), pages 404-408, June.
  17. Derks, Jean J M & Gilles, Robert P, 1995. "Hierarchical Organization Structures and Constraints on Coalition Formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 147-63.
  18. repec:hal:journl:halshs-00445171 is not listed on IDEAS
  19. van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 255-68.
  20. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print halshs-00581662, HAL.
  21. Hans Reijnierse & Jean Derks, 1998. "Note On the core of a collection of coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 451-459.
  22. Ulrich Faigle & Michel Grabisch, 2011. "A Discrete Choquet Integral for Ordered Systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00563926, HAL.
  23. Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June.
  24. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00445171. 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.