TY - JOUR
T1 - Weak differential marginality and the Shapley value
AU - Casajus, André
AU - Yokote, Koji
N1 - Funding Information:
We are grateful to Yukihiko Funaki and Frank Huettner as well as to a referee and an associate editor for valuable comments on this paper. Financial support by the Deutsche Forschungsgemeinschaft for Andr? Casajus (grant CA 266/4-1) and by the Japan Society for the Promotion of Science (JSPS) for Koji Yokote is gratefully acknowledged.
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ marginal contributions to coalitions containing neither of them does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show that this characterization can be improved by using a substantially weaker property than differential marginality. Weak differential marginality requires two players’ payoffs to change in the same direction when these players’ marginal contributions to coalitions containing neither of them change by the same amount.
AB - The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ marginal contributions to coalitions containing neither of them does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show that this characterization can be improved by using a substantially weaker property than differential marginality. Weak differential marginality requires two players’ payoffs to change in the same direction when these players’ marginal contributions to coalitions containing neither of them change by the same amount.
KW - Differential marginality
KW - Shapley value
KW - TU game
KW - Weak differential marginality
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U2 - 10.1016/j.jet.2016.11.007
DO - 10.1016/j.jet.2016.11.007
M3 - Article
AN - SCOPUS:85008616128
VL - 167
SP - 274
EP - 284
JO - Journal of Economic Theory
JF - Journal of Economic Theory
SN - 0022-0531
ER -