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Symmetry, mutual dependence, and the weighted Shapley values

  • We pinpoint the position of the (symmetric) Shapley value within the class of positively weighted Shapley values to their treatment of symmetric versus mutually dependent players. While symmetric players are equally productive, mutually dependent players are only jointly (hence, equally) productive. In particular, we provide a characterization of the whole class of positively weighted Shapley values that uses two standard properties, efficiency and the null player out property, and a new property called superweak differential marginality. Superweak differential marginality is a relaxation of weak differential marginality (Casajus and Yokote, J Econ Theory 167, 2017, 274-284). It requires two players' payoff for two games to change in the same direction whenever only their joint productivity changes, i.e., their individual productivities stay the same. In contrast, weak differential marginality already requires this when their individual productivities change by the same amount. The Shapley value is the unique positively weighted Shapley value that satisfies weak differential marginality.

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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 (171)
Year of Completion:2018
Page Number:19
Tag:TU game; mutual dependence; superweak differential monotonicity; symmetry; weak differential monotonicity; weighted Shapley values
Content Focus:Academic Audience
Licence (German):License LogoUrheberrechtlich geschützt