Decompositions of inequality measures from the perspective of the Shapley–Owen value

Rodrigue Tido Takeng (), Arnold Cedrick Soh Voutsa () and Kévin Fourrey ()
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Rodrigue Tido Takeng: CREM (CNRS 6211), Normandie University, UNICAEN
Arnold Cedrick Soh Voutsa: THEMA (CNRS 8184), CY Cergy Paris Université
Kévin Fourrey: ERUDITE, CEET(CNAM), UPEC

Theory and Decision, 2023, vol. 94, issue 2, No 6, 299-331

Abstract: Abstract This article proposes three new decompositions of inequality measures, drawn from the framework of cooperative game theory. It allows the impact of players’ interactions, rather than players’ contributions to inequality, to be taken into consideration. These innovative approaches are especially suited for the study of income inequality when the income has a hierarchical structure: the income is composed of several primary sources, with the particularity that each of them is also composed of secondary sources. We revisit the Shapley–Owen value that quantifies the importance of each of these secondary sources in the overall income inequality. Our main contribution is to decompose this importance into two parts: the pure marginal contribution of the considered source and a weighted sum of pairwise interactions. We then provide an axiomatic characterization of each additive interaction decomposable (AID) coalitional value considered in this paper. We give an application of these decompositions in the context of inequality theory.

Keywords: Game theory; Hierarchical structures; Axiomatic characterization; AID; Inequality measures; Shapley–Owen value (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11238-022-09893-w

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