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The lattice structure of the S-Lorenz core

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  • Vincent Iehlé

Abstract

For any TU game and any ranking of players, the set of all preimputations compatible 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):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. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Vincent Iehlé, 2015. "The lattice structure of the S-Lorenz core," Theory and Decision, Springer, vol. 78(1), pages 141-151, January.
    • Handle: RePEc:kap:theord:v:78:y:2015:i:1:p:141-151
    DOI: 10.1007/s11238-014-9415-6
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    More about this item

    Keywords

    Constrained egalitarian allocation; Cooperative game; Lattice; Lorenz core; Lorenz order; C71; D63;
    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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