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Income inequality games

Abstract

The paper explores different applications of the Shapley value for either inequality or poverty measures. We first investigate the problem of source decomposition of inequality measures, the so-called additive income sources inequality games, based on the Shapley value, introduced by Chantreuil and Trannoy (1999) and Shorrocks (1999). We show that multiplicative inequality games provide dual results compared with Chantreuil and Trannoy’s ones. We also investigate the case of multiplicative poverty games for which indices are non additively decomposable in order to capture contributions of sub-indices, which are multiplicatively connected with, as in the Sen-Shorrocks-Thon poverty index. We finally show, in the case of additive poverty indices, that the Shapley value may be equivalent to traditional methods of decomposition such as subgroup consistency and additive decomposition.

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Correspondence to Stéphane Mussard.

Additional information

This work has been partially supported by the AXA Chair on Large Risks in Insurance (Fondation du Risque).

Part of this paper was presented at Cornell University, Ithaca, NY, “Inequality: New Directions”.

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Charpentier, A., Mussard, S. Income inequality games. J Econ Inequal 9, 529–554 (2011). https://doi.org/10.1007/s10888-011-9184-1

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  • DOI: https://doi.org/10.1007/s10888-011-9184-1

Keywords

  • Inequality
  • Poverty
  • Shapley
  • Source decomposition
  • Subgroup decomposition

JEL Clasification

  • D31
  • D63