Coalition structures induced by the strength of a graph
We study cooperative games associated with a communication structure which takes into account a level of communication between players. Let us consider an undirected communication graph: each node represents a player and there is an edge between two nodes if the corresponding players can communicate directly. Moreover we suppose that a weight is associated with each edge. We compute the so-called strength of this graph and use the corresponding partition to determine a particular coalition structure. The strength of a graph is a measure introduced in graph theory to evaluate the resistance of networks under attacks. It corresponds to the minimum on all subsets of edges of the ratio between the sum of the weights of the edges and the number of connected components created when the set of edges is suppressed from the graph. The set of edges corresponding to the minimum ratio induces a partition of the graph. We can iterate the calculation of the strength on the subgraphs of the partition to obtain refined partitions which we use to define a hierarchy of coalition structures. For a given game on the graph, we build new games induced by these coalition structures and study the inheritance of convexity properties, and the Shapley value associated with them.
|Date of creation:||Jul 2011|
|Date of revision:|
|Contact details of provider:|| Postal: 106-112 boulevard de l'Hôpital 75 647 PARIS CEDEX 13|
Phone: + 33 44 07 81 00
Fax: + 33 1 44 07 83 01
Web page: http://centredeconomiesorbonne.univ-paris1.fr/
More information through EDIRC
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.:
- van den Nouweland, Anne & Borm, Peter, 1991.
"On the Convexity of Communication Games,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 19(4), pages 421-30.
- Michel Grabisch, 2013.
"The core of games on ordered structures and graphs,"
Annals of Operations Research,
Springer, vol. 204(1), pages 33-64, April.
- Michel Grabisch, 2013. "The core of games on ordered structures and graphs," PSE - Labex "OSE-Ouvrir la Science Economique" hal-00803233, HAL.
- Michel Grabisch, 2009. "The core of games on ordered structures and graphs," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445171, HAL.
When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:11059. 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: (Lucie Label)
If references are entirely missing, you can add them using this form.