Fair economic division: how to modify Shapley value to take into account the fact that different people have different productivity

Christian Servin and Vladik Kreinovich

Asian Journal of Economics and Banking, 2025, vol. 9, issue 2, 213-221

Abstract: PurposeWhen several participants, working together, gained some amount of money, what is the fair way to distribute this amount between them? This is the problem that the future Nobelist Lloyd Shapley was working on when he proposed what is now called the Shapley value – a division uniquely determined by natural fairness assumptions. However, this solutions is not universal: it assumes that all participants are equal – in particular, that they have equal productivity. In practice, people have different productivity levels, and these productivity levels can differ a lot: for example, some software engineers are several times more productive than others. It is desirable to take this difference in productivity into account.Design/methodology/approachShapley value is based on an axiomatic approach: it is uniquely determined by the appropriate fairness assumptions. To generalize Shapley value to the case of different productivity, we modified these assumptions appropriately, and analyzed what can be derived from these modified assumptions.FindingsWe prove that there is a unique division scheme that satisfies all the resulting assumptions. This scheme is thus a generalization of Shapley value to this more general and more realistic situation, when different participants have different productivities.Originality/valueBoth the formulation of the problem and the result are new. The resulting division scheme can be used to more adequately distribute the common gains – by explicitly taking into account the fact that different participants have, in general, different productivities.

Keywords: Shapley value; Fair distribution; Difference in productivity; Axiomatic approach (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eme:ajebpp:ajeb-12-2024-0150

DOI: 10.1108/AJEB-12-2024-0150

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