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A non-parametric approach to testing the axioms of the Shapley value with limited data

Victor H. Aguiar, Roland Pongou () and Jean-Baptiste Tondji

Games and Economic Behavior, 2018, vol. 111, issue C, 41-63

Abstract: The unique properties of the Shapley value–efficiency, equal treatment of identical input factors, and marginality–have made it an appealing solution concept in various classes of problems. It is however recognized that the pay schemes utilized in many real-life situations generally depart from this value. We propose a non-parametric approach to testing the empirical content of this concept with limited datasets. We introduce the Shapley distance, which, for a fixed monotone transferable-utility game, measures the distance of an arbitrary pay profile to the Shapley pay profile, and show that it is additively decomposable into the violations of the classical Shapley axioms. The analysis has several applications. In particular, it can be used to assess the extent to which an income distribution can be considered fair or unfair, and whether any particular case of unfairness is due to the violation of one or a combination of the Shapley axioms.

Keywords: Shapley value; Fairness violations; Limited data; Inequality; Shapley distance (search for similar items in EconPapers)
JEL-codes: C71 C78 D20 D30 J30 (search for similar items in EconPapers)
Date: 2018
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