Axiomatizations of the Shapley value for games on augmenting systems
This paper deals with cooperative games in which only certain coalitions are allowed to form. There have been previous models developed to confront the problem of unallowable coalitions. Games restricted by a communication graph were introduced by Myerson and Owen. In their model, the feasible coalitions are those that induce connected subgraphs. Another type of model is introduced in Gilles, Owen and van den Brink. In their model, the possibilities of coalition formation are determined by the positions of the players in a so-called permission structure. Faigle proposed another model for cooperative games defined on lattice structures. We introduce a combinatorial structure called augmenting system which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph. In this framework, the Shapley value of games on augmenting systems is introduced and two axiomatizations of this value are showed.
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.:
- Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
- 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.
- Bilbao, J. M., 1998. "Axioms for the Shapley value on convex geometries," European Journal of Operational Research, Elsevier, vol. 110(2), pages 368-376, October.
- Gilles, R.P. & Owen, G. & van den Brink, J.R., 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.
- 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.
- Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:196:y:2009:i:3:p:1008-1014. 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: (Zhang, Lei)
If references are entirely missing, you can add them using this form.