The core of games on distributive lattices : how to share benefits in a hierarchy
AbstractFinding 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, it is not obvious to define a suitable notion of core, reflecting the team structure, and previous attempts are not satisfactory in this respect. We propose a new notion of core, which imposes efficiency of the allocation at each level of the hierarchy, 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 InfoIf 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.
Bibliographic InfoPaper provided by HAL in its series Post-Print with number halshs-00344802.
Date of creation: Oct 2008
Date of revision:
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00344802
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
Cooperative game; feasible coalition; core; hierarchy.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-12-14 (All new papers)
- NEP-CDM-2008-12-14 (Collective Decision-Making)
- NEP-GTH-2008-12-14 (Game Theory)
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.:
- Hans Reijnierse & Jean Derks, 1998. "Note On the core of a collection of coalitions," International Journal of Game Theory, Springer, vol. 27(3), pages 451-459.
- Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
- Gilles, R.P. & Owen, G. & Brink, J.R. van den, 1991.
"Games with permission structures: The conjunctive approach,"
1991-14, Tilburg University, Center for Economic Research.
- Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, vol. 20(3), pages 277-93.
- 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.
- Gabrielle Demange, 2004.
"On Group Stability in Hierarchies and Networks,"
Journal of Political Economy,
University of Chicago Press, vol. 112(4), pages 754-778, August.
- Bilbao, J. M. & Lebron, E. & Jimenez, N., 1999. "The core of games on convex geometries," European Journal of Operational Research, Elsevier, vol. 119(2), pages 365-372, December.
- Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, vol. 21(3), pages 249-66.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If references are entirely missing, you can add them using this form.