Some values for constant-sum and bilateral cooperative games

Andrzej Młodak. "Some values for constant-sum and bilateral cooperative games." Applicationes Mathematicae 34.3 (2007): 359-371. <http://eudml.org/doc/279976>.

@article{AndrzejMłodak2007,
abstract = {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.},
author = {Andrzej Młodak},
journal = {Applicationes Mathematicae},
keywords = {cooperative game; constant-sum game; bilateral game; value; Banzhaf value; Deegan–Packel value},
language = {eng},
number = {3},
pages = {359-371},
title = {Some values for constant-sum and bilateral cooperative games},
url = {http://eudml.org/doc/279976},
volume = {34},
year = {2007},
}

TY - JOUR
AU - Andrzej Młodak
TI - Some values for constant-sum and bilateral cooperative games
JO - Applicationes Mathematicae
PY - 2007
VL - 34
IS - 3
SP - 359
EP - 371
AB - 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.
LA - eng
KW - cooperative game; constant-sum game; bilateral game; value; Banzhaf value; Deegan–Packel value
UR - http://eudml.org/doc/279976
ER -