We prove new axiomatizations of the Shapley value and the Banzhaf value, defined on the class of nonnegative constant-sum games with nonzero worth of the grand coalition as well as on nonnegative bilateral games with nonzero worth of the grand coalition. A characteristic feature of the latter class of cooperative games is that for such a game any coalition and its complement in the set of all players have the same worth. The axiomatizations are then generalized to the entire class of constant-sum or bilateral games, respectively. Moreover, a new axiomatization of the Deegan-Packel value on the set of all cooperative games is presented and possibilities of creation of its version in those special cases are discussed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-7,
author = {Andrzej M\l odak},
title = {Some values for constant-sum and bilateral cooperative games},
journal = {Applicationes Mathematicae},
volume = {34},
year = {2007},
pages = {359-371},
zbl = {1130.91304},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-7}
}
Andrzej Młodak. Some values for constant-sum and bilateral cooperative games. Applicationes Mathematicae, Tome 34 (2007) pp. 359-371. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am34-3-7/