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.
Document Type: | Article |
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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): | ![]() |