Axiomatizations of the normalized Banzhaf value and the Shapley value
Gerard van der Laan and
Rene van den Brink ()
Social Choice and Welfare, 1998, vol. 15, issue 4, 567-582
Abstract:
A cooperative game with transferable utilities - or simply a TU-game - describes a situation in which players can obtain certain payoffs by cooperation. A solution concept for these games is a function which assigns to every such a game a distribution of payoffs over the players in the game. Famous solution concepts for TU-games are the Shapley value and the Banzhaf value. Both solution concepts have been axiomatized in various ways. An important difference between these two solution concepts is the fact that the Shapley value always distributes the payoff that can be obtained by the `grand coalition' consisting of all players cooperating together while the Banzhaf value does not satisfy this property, i.e., the Banzhaf value is not efficient. In this paper we consider the normalized Banzhaf value which distributes the payoff that can be obtained by the `grand coalition' proportional to the Banzhaf values of the players. This value does not satisfy certain axioms underlying the Banzhaf value. In this paper we introduce some new axioms that characterize the normalized Banzhaf value. We also provide an axiomatization of the Shapley value using similar axioms.
Date: 1998-08-06
Note: Received: 10 April 1996 / Accepted: 2 June 1997
References: Add references at CitEc
Citations: View citations in EconPapers (41)
Downloads: (external link)
http://link.springer.de/link/service/journals/00355/papers/8015004/80150567.pdf (application/pdf)
http://link.springer.de/link/service/journals/0035 ... 15004/80150567.ps.gz (application/postscript)
Access to the full text of the articles in this series is restricted
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:spr:sochwe:v:15:y:1998:i:4:p:567-582
Ordering information: This journal article can be ordered from
http://www.springer. ... c+theory/journal/355
Access Statistics for this article
Social Choice and Welfare is currently edited by Bhaskar Dutta, Marc Fleurbaey, Elizabeth Maggie Penn and Clemens Puppe
More articles in Social Choice and Welfare from Springer, The Society for Social Choice and Welfare Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().