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The lattice structure of the S-Lorenz core

Author

Listed:
  • Vincent Iehlé

    (LEDa - Laboratoire d'Economie de Dauphine - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

For any TU game and any ranking of players, the set of all preimputations compat- ible with the ranking, equipped with the Lorenz order, is a bounded join semi-lattice. Furthermore the set admits as sublattice the S-Lorenz core intersected with the region compatible with the ranking. This result uncovers a new property about the structure of the S-Lorenz core. As immediate corollaries we obtain complementary results to the findings of Dutta and Ray, Games Econ. Behav., 3(4) p. 403-422 (1991), by showing that any S-constrained egalitarian allocation is the (unique) Lorenz greatest element of the S-Lorenz core on the rank-preserving region the allocation belongs to. Besides, our results suggest that the comparison between W- and S-constrained egalitarian allocations is more puzzling than what is usually admitted in the literature.

Suggested Citation

  • Vincent Iehlé, 2015. "The lattice structure of the S-Lorenz core," Post-Print halshs-00846826, HAL.
    • Handle: RePEc:hal:journl:halshs-00846826
    DOI: 10.1007/s11238-014-9415-6
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00846826v2
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    References listed on IDEAS

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    More about this item

    Keywords

    Lorenz criterion; Lorenz core; cooperative game; constrained egalitarian allocation; lattice;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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