TY  - JOUR
U1  - Wissenschaftlicher Artikel
A1  - Casajus, André
T1  - Symmetry, mutual dependence, and the weighted Shapley values
JF  - Journal of economic theory
N2  - We pinpoint the position of the (symmetric) Shapley value within the class of positively weighted Shapley values to their treatment of symmetric versus mutually dependent players. While symmetric players are equally productive, mutually dependent players are only jointly (hence, equally) productive. In particular, we provide a characterization of the whole class of positively weighted Shapley values that uses two standard properties, efficiency and the null player out property, and a new property called superweak differential marginality. Superweak differential marginality is a relaxation of weak differential marginality (Casajus and Yokote, J Econ Theory 167, 2017, 274-284). It requires two players' payoff for two games to change in the same direction whenever only their joint productivity changes, i.e., their individual productivities stay the same. In contrast, weak differential marginality already requires this when their individual productivities change by the same amount. The Shapley value is the unique positively weighted Shapley value that satisfies weak differential marginality.
KW  - TU game
KW  - Weighted Shapley values
KW  - Symmetry
KW  - Mutual dependence
KW  - Weak differential marginality
KW  - Superweak differential marginality
Y1  - 2018
SN  - 0022-0531
SS  - 0022-0531
U6  - https://doi.org/10.1016/j.jet.2018.09.001
DO  - https://doi.org/10.1016/j.jet.2018.09.001
VL  - 178
IS  - November 2018
SP  - 105
EP  - 123
ER  -