Abstract
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.
Original language | English |
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Pages (from-to) | 274-284 |
Number of pages | 11 |
Journal | Journal of Economic Theory |
Volume | 167 |
DOIs | |
Publication status | Published - 2017 Jan 1 |
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Keywords
- Differential marginality
- Shapley value
- TU game
- Weak differential marginality
ASJC Scopus subject areas
- Economics and Econometrics
Cite this
Weak differential marginality and the Shapley value. / Casajus, André; Yokote, Koji.
In: Journal of Economic Theory, Vol. 167, 01.01.2017, p. 274-284.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Weak differential marginality and the Shapley value
AU - Casajus, André
AU - Yokote, Koji
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
UR - http://www.scopus.com/inward/record.url?scp=85008616128&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85008616128&partnerID=8YFLogxK
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 -