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

Authors

Victor H. Aguiar
Roland Pongou
Jean-Baptiste Tondji, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

9-2018

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.

Comments

Original published version available at https://doi.org/10.1016/j.geb.2018.06.003

Recommended Citation

Aguiar, V.H., Pongou, R. and Tondji, J.B., 2018. A non-parametric approach to testing the axioms of the Shapley value with limited data. Games and Economic Behavior, 111, pp.41-63. https://doi.org/10.1016/j.geb.2018.06.003

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Games and Economic Behavior

DOI

10.1016/j.geb.2018.06.003