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Relaxations of symmetry and the weighted Shapley values

André Casajus

Economics Letters, 2019, vol. 176, issue C, 75-78

Abstract: We revisit Kalai and Samet’s (1987) 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.

Keywords: TU game; Weighted Shapley values; Sign symmetry; Mutual dependence; Weak sign symmetry; Superweak sign symmetry (search for similar items in EconPapers)
JEL-codes: C71 D60 (search for similar items in EconPapers)
Date: 2019
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