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

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  • Aguiar, Victor H.
  • Pongou, Roland
  • Tondji, Jean-Baptiste

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.

Suggested Citation

  • Aguiar, Victor H. & Pongou, Roland & Tondji, Jean-Baptiste, 2018. "A non-parametric approach to testing the axioms of the Shapley value with limited data," Games and Economic Behavior, Elsevier, vol. 111(C), pages 41-63.
    • Handle: RePEc:eee:gamebe:v:111:y:2018:i:c:p:41-63
    DOI: 10.1016/j.geb.2018.06.003
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    2. Chessa, Michela & Hanaki, Nobuyuki & Lardon, Aymeric & Yamada, Takashi, 2023. "An experiment on the Nash program: A comparison of two strategic mechanisms implementing the Shapley value," Games and Economic Behavior, Elsevier, vol. 141(C), pages 88-104.
    3. repec:dpr:wpaper:1221 is not listed on IDEAS
    4. Steffen Limmer, 2023. "Empirical Study of Stability and Fairness of Schemes for Benefit Distribution in Local Energy Communities," Energies, MDPI, vol. 16(4), pages 1-16, February.
    5. Ghislain H. Demeze-Jouatsa & Roland Pongou & Jean-Baptiste Tondji, 2021. "A Free and Fair Economy: A Game of Justice and Inclusion," Papers 2107.12870, arXiv.org.
    6. Michela Chessa & Nobuyuki Hanaki & Aymeric Lardon & Takashi Yamada, 2023. "An Experiment on Demand Commitment Bargaining," Dynamic Games and Applications, Springer, vol. 13(2), pages 589-609, June.
    7. Michela Chessa & Nobuyuki Hanaki & Aymeric Lardon & Takashi Yamada, 2023. "An Experimental Nash Program: A Comparison of Structured v.s. Semi-Structured Bargaining Experiments," ISER Discussion Paper 1221r, Institute of Social and Economic Research, Osaka University, revised Sep 2024.
    8. Pongou, Roland & Tondji, Jean-Baptiste, 2024. "The reciprocity set," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    9. Demeze-Jouatsa, Ghislain-Herman & Pongou, Roland & Tondji, Jean-Baptiste, 2021. "A Free and Fair Economy: A Game of Justice and Inclusion," Center for Mathematical Economics Working Papers 653, Center for Mathematical Economics, Bielefeld University.
    10. Pongou, Roland & Tchantcho, Bertrand, 2021. "Round-robin political tournaments: Abstention, truthful equilibria, and effective power," Games and Economic Behavior, Elsevier, vol. 130(C), pages 331-351.
    11. Ghislain Herman Demeze-Jouatsa & Roland Pongou & Jean-Baptiste Tondji, 2024. "Justice, inclusion, and incentives," Journal of Theoretical Politics, , vol. 36(2), pages 101-131, April.
    12. Victor H. Aguiar & Roland Pongou & Roberto Serrano & Jean-Baptiste Tondji, 2018. "An Index of Unfairness," Working Papers 2018-9, Brown University, Department of Economics.

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    More about this item

    Keywords

    Shapley value; Fairness violations; Limited data; Inequality; Shapley distance;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D20 - Microeconomics - - Production and Organizations - - - General
    • D30 - Microeconomics - - Distribution - - - General
    • J30 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - General

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