TY  - JOUR
U1  - Wissenschaftlicher Artikel
A1  - Casajus, André
A1  - Yokote, Koji
T1  - Weakly differentially monotonic solutions for cooperative games
JF  - International journal of game theory
N2  - The principle of differential monotonicity for cooperative games states that the differential of two players' payoffs weakly increases whenever the differential of these players' marginal contributions to coalitions containing neither of them weakly increases. Together with the standard efficiency property and a relaxation of the null player property, differential monotonicity characterizes the egalitarian Shapley values, i.e., the coex mixtures of the Shapley value and the equal division value for games with more than two players. For games that contain more than three players, we show that, cum grano salis, this characterization can be improved by using a substantially weaker property than differential monotonicity. Weak differential monotonicity refers to two players in situations where one player's change of marginal contributions to coalitions containing neither of them is weakly greater than the other player's change of these marginal contributions. If, in such situations, the latter player's payoff weakly/strictly increases, then the former player's payoff also weakly/strictly increases.
KW  - TU game
KW  - Shapley value
KW  - Differential marginality
KW  - Weak differential marginality
Y1  - 2019
SN  - 0020-7276
SS  - 0020-7276
U6  - https://doi.org/10.1007/s00182-019-00669-1
DO  - https://doi.org/10.1007/s00182-019-00669-1
VL  - 48
SP  - 979
EP  - 997
ER  -