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 -