An Axiomatization of the Banzhaf Value for Cooperative Games on Antimatroids
AbstractCooperative games on antimatroids are cooperative games restricted by a combinatorial structure which generalize the permission structure. So, cooperative games on antimatroids group several well-known families of games which have important applications in economics and politics. Therefore, the study of the restricted games by antimatroids allows to unify criteria of various lines of research. The current paper establishes axioms that determine the restricted Banzhaf value on antimatroids by conditions on the cooperative game and the structure determined by the antimatroid. The set of given axioms generalize the axiomatizations given for the Banzhaf permission values. We also give an axomatization of the restricted Banzhaf value for the smaller class of poset antimatroids. Finally, we apply the above results to auction situations.
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 Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 02-110/1.
Date of creation: 30 Oct 2002
Date of revision:
Contact details of provider:
Web page: http://www.tinbergen.nl
Cooperative game; antimatroid; permission structure; Banzhaf value.;
Other versions of this item:
- E. Algaba & J. M. Bilbao & R. van den Brink & A. Jiménez-Losada, 2004. "An axiomatization of the Banzhaf value for cooperative games on antimatroids," Computational Statistics, Springer, Springer, vol. 59(1), pages 147-166, 02.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Kamijo, Yoshio & Kongo, Takumi, 2012. "Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value," European Journal of Operational Research, Elsevier, Elsevier, vol. 216(3), pages 638-646.
- Rene van den Brink & Chris Dietz, 2012.
"Games with a Local Permission Structure: Separation of Authority and Value Generation,"
Tinbergen Institute Discussion Papers, Tinbergen Institute
12-126/II, Tinbergen Institute.
- René Brink & Chris Dietz, 2014. "Games with a local permission structure: separation of authority and value generation," Theory and Decision, Springer, Springer, vol. 76(3), pages 343-361, March.
- René Brink, 2010. "Axiomatizations of Banzhaf permission values for games with a permission structure," International Journal of Game Theory, Springer, Springer, vol. 39(3), pages 445-466, July.
- Matthew Ryan, 2010. "Mixture sets on finite domains," Decisions in Economics and Finance, Springer, Springer, vol. 33(2), pages 139-147, November.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Antoine Maartens (+31 626 - 160 892)).
If references are entirely missing, you can add them using this form.