1. Decompositions of inequality measures from the perspective of the Shapley–Owen value
- Author
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Arnold Cedrick Soh Voutsa, Rodrigue Tido Takeng, Kévin Fourrey, Centre de recherche en économie et management (CREM), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-Université de Rennes (UR)-Centre National de la Recherche Scientifique (CNRS), Théorie économique, modélisation et applications (THEMA), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), Equipe de Recherche sur l’Utilisation des Données Individuelles en lien avec la Théorie Economique (ERUDITE), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Université Gustave Eiffel, CY Cergy Paris Universite [ANR-16-IDEX-008], ANR-16-IDEX-0008,PSI,PSI(2016), Normandie Université (NU)-Normandie Université (NU)-Université de Rennes 1 (UR1), and Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Hierarchical structures ,Inequality measures ,Shapley-Owen value ,Inequality ,media_common.quotation_subject ,Structure (category theory) ,General Decision Sciences ,Context (language use) ,Economic inequality ,Arts and Humanities (miscellaneous) ,AID ,Developmental and Educational Psychology ,Game theory ,Axiom ,Applied Psychology ,Mathematics ,media_common ,Axiomatic characterization ,General Social Sciences ,Cooperative game theory ,[SHS.ECO]Humanities and Social Sciences/Economics and Finance ,Computer Science Applications ,Value (mathematics) ,Mathematical economics ,General Economics, Econometrics and Finance - Abstract
International audience; 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.
- Published
- 2022
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