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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 modern version of 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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Document Type:Working Paper
Author:André CasajusORCiD
Chairs and Professorships:Chair of Economics and Information Systems
Parent Title (English):HHL Working Paper
Series (Serial Number):HHL-Arbeitspapier / HHL Working paper (175)
Year of Completion:2018
Page Number:9
Tag:TU game; mutual dependence; sign symmetry; superweak sign symmetry; weak di§erential monotonicity; weak sign symmetry; weighted Shapley values
Content Focus:Academic Audience
Licence (German):License LogoUrheberrechtlich geschützt