The lattice structure of the S-Lorenz core
Iehlé, Vincent (2015), The lattice structure of the S-Lorenz core, Theory and Decision, 78, 1, p. 141-151. http://dx.doi.org/10.1007/s11238-014-9415-6
TypeArticle accepté pour publication ou publié
External document linkhttp://halshs.archives-ouvertes.fr/halshs-00846826
Journal nameTheory and Decision
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Abstract (EN)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.
Subjects / Keywordslattice; constrained egalitarian allocation; cooperative game; Lorenz-core; Lorenz criterion
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