Applying the Owen construction of value of games with a priori unions to the normalized Banzhaf value gives a new type of the normalized Banzhaf value for games with a priori unions. Using a simple example of a four-person voting game with a priori unions, it is shown that this value is different from those known in the literature: the normalized Owen-Banzhaf value, the Banzhaf share function defined by van der Laan and van den Brink and the Banzhaf index for simple games with a priori unions introduced by Malawski. Thus, all four notions are distinct.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-22,
author = {Honorata Sosnowska},
title = {Four different approaches to the normalized Banzhaf values of games with a priori unions},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {267-273},
zbl = {1255.91029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-22}
}
Honorata Sosnowska. Four different approaches to the normalized Banzhaf values of games with a priori unions. Banach Center Publications, Tome 72 (2006) pp. 267-273. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc71-0-22/