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Relaxations of symmetry and the weighted Shapley values

  • 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 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.

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Metadaten
Document Type:Article
Language:English
Author:André Casajus
Chairs and Professorships:Chair of Economics and Information Systems
DOI:https://doi.org/10.1016/j.econlet.2018.12.031
Parent Title (English):Economics letters
ISSN:0165-1765
Volume:176
Issue:March 2019
Year of Completion:2019
First Page:75
Last Page:78
Tag:Mutual dependence; Sign symmetry; Superweak sign symmetry; TU game; Weak sign symmetry; Weighted Shapley values
Content Focus:Academic Audience
Peer Reviewed:Yes
Rankings:AJG Ranking / 3
VHB Ranking / B
SJR Ranking / Q2
Licence (German):License LogoUrheberrechtlich geschützt