TY  - RPRT
U1  - Arbeitspapier
A1  - Casajus, André
T1  - Relaxations of symmetry and the weighted Shapley values
T2  - HHL Working Paper
N2  - We revisit Kalai and Samet's (Int J Game Theory 16, 1987, 205--222) first characterization of the class of weighted Shapley values. While keeping efficiency, additivity, and the null player property from the modern version of the original characterization of the symmetric Shapley value, they replace symmetry with positivity and partnership consistency. The latter two properties, however, are neither implied by nor related to symmetry. We suggest relaxations of symmetry that together with efficiency, additivity, and the null player property characterize classes of weighted Shapley values. For example, weak sign symmetry requires the payoffs of mutually dependent players to have the same sign. Mutually dependent players are symmetric players whose marginal contributions to coalitions containing neither of them are zero.
T3  - HHL-Arbeitspapier / HHL Working paper - 175 
KW  - TU game
KW  - weighted Shapley values
KW  - sign symmetry
KW  - mutual dependence
KW  - weak sign symmetry
KW  - superweak sign symmetry
KW  - weak di§erential monotonicity
Y1  - 2018
U6  - https://nbn-resolving.org/urn:nbn:de:0217-23466
UN  - https://nbn-resolving.org/urn:nbn:de:0217-23466
SP  - 9
S1  - 9
ER  -