Characterizing Distributive Principles in Hierarchies with an Application to Wage Design

David Lowing () and Satoshi Nakada
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David Lowing: CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, ENS Rennes - École normale supérieure - Rennes
Satoshi Nakada: Tokyo University of Science

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Abstract: We study the allocation of surplus in hierarchical organizations when marginalism, hierarchical marginalism, and egalitarianism conflict. We represent these principles by the Shapley, Permission, and Equal Division values and introduce their convex combinations, which we call Egalitarian Shapley-Permission values. We provide an axiomatic characterization of this family by first characterizing a broader class whose weights may vary across coalitions, and then identify the conditions under which these weights must be common across unanimity components. Applying the family to wage design in a hierarchical firm, we show that the manager-to-worker wage ratio is bounded above by the manager's span of control, and that a manager is paid at least as much as each worker for every degree of input substitutability if and only if the Shapley component receives zero weight. In large organizations with nearly complementary worker inputs, the managerial premium depends jointly on span of control and input substitutability.

Keywords: Egalitarianism; Marginalism; Hierarchical marginalism; Axiomatic method; Cooperative games; Wage allocation (search for similar items in EconPapers)
Date: 2026-09-02
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