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Multidimensional inequalities and generalized quantile functions

Author

Listed:
  • Sinem Bas

    (Université Catholique de Louvain, CORE)

  • Philippe Bich

    (Université Paris 1 Panthéon Sorbonne UMR 8074)

  • Alain Chateauneuf

    (Université Paris 1 Panthéon Sorbonne UMR 8074)

Abstract

In this paper, we extend the generalized Yaari’s dual theory for multidimensional distributions, in the vein of Galichon and Henry’s paper (Galichon and Henry in J Econ Theory 147:1501–1516, 2012). We show how a class of generalized quantiles—which encompasses Galichon and Henry’s one or multivariate quantile transform [see Arjas and Lehtonen (Math Oper Res 3(3):205–223, 1978), O’Brien (Ann Prob 3(1):80–88, 1975) or Ruschendorf (Ann Probab 9(2):276–283, 1981)]—allows to derive a general representation theorem.

Suggested Citation

  • Sinem Bas & Philippe Bich & Alain Chateauneuf, 2021. "Multidimensional inequalities and generalized quantile functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 375-409, March.
    • Handle: RePEc:spr:joecth:v:71:y:2021:i:2:d:10.1007_s00199-020-01253-5
    DOI: 10.1007/s00199-020-01253-5
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    1. Carlier, G. & Dana, R.-A. & Galichon, A., 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," Journal of Economic Theory, Elsevier, vol. 147(1), pages 207-229.
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    More about this item

    Keywords

    Multidimensional distributions; Quantile; Inequality; Optimal coupling;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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