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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Rodrigue Tido Takeng & Arnold Cedrick Soh Voutsa & Kévin Fourrey, 2023. "Decompositions of inequality measures from the perspective of the Shapley–Owen value," Theory and Decision, Springer, vol. 94(2), pages 299-331, February.
    • Handle: RePEc:kap:theord:v:94:y:2023:i:2:d:10.1007_s11238-022-09893-w
    DOI: 10.1007/s11238-022-09893-w
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