The lattice structure of the S-Lorenz core

Vincent Iehlé

Theory and Decision, 2015, vol. 78, issue 1, 151 pages

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

Keywords: Constrained egalitarian allocation; Cooperative game; Lattice; Lorenz core; Lorenz order; C71; D63 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11238-014-9415-6

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