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The lattice structure of the S-Lorenz core

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  • Vincent Iehlé

    ()
    (LEDa - Laboratoire d'Economie de Dauphine - Université Paris IX - Paris Dauphine, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)

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.

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Paper provided by HAL in its series Working Papers with number halshs-00846826.

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Date of creation: 01 Jan 2014
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Handle: RePEc:hal:wpaper:halshs-00846826

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Keywords: Lorenz criterion; Lorenz core; cooperative game; constrained egalitarian allocation; lattice;

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  1. Ashish Goel & Adam Meyerson & Thomas Weber, 2009. "Fair welfare maximization," Economic Theory, Springer, vol. 41(3), pages 465-494, December.
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