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Axiomatic characterization of pointwise Shapley decompositions

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  • Marcus C Christiansen

Abstract

A common problem in various applications is the additive decomposition of the output of a function with respect to its input variables. Functions with binary arguments can be axiomatically decomposed by the famous Shapley value. For the decomposition of functions with real arguments, a popular method is the pointwise application of the Shapley value on the domain. However, this pointwise application largely ignores the overall structure of functions. In this paper, axioms are developed which fully preserve functional structures and lead to unique decompositions for all Borel measurable functions.

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  • Marcus C Christiansen, 2023. "Axiomatic characterization of pointwise Shapley decompositions," Papers 2303.07773, arXiv.org.
    • Handle: RePEc:arx:papers:2303.07773
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    References listed on IDEAS

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    1. Fortin, Nicole & Lemieux, Thomas & Firpo, Sergio, 2011. "Decomposition Methods in Economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 1, pages 1-102, Elsevier.
    2. Gero Junike & Hauke Stier & Marcus C. Christiansen, 2022. "Profit and loss decomposition in continuous time and approximations," Papers 2212.06733, arXiv.org, revised Dec 2024.
    3. Nicholas Moehle & Stephen Boyd & Andrew Ang, 2021. "Portfolio Performance Attribution via Shapley Value," Papers 2102.05799, arXiv.org.
    4. Anthony Shorrocks, 2013. "Decomposition procedures for distributional analysis: a unified framework based on the Shapley value," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(1), pages 99-126, March.
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