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Median matchings and farsighted stability: two papers on matching| old_uid | 9421 |
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| title | Median matchings and farsighted stability: two papers on matching |
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| start_date | 2010/12/13 |
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| schedule | 14h30 |
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| online | no |
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| location_info | Salle A707 |
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| summary | The talk is based on two papers. Paper 1: Smith and Rawls Share a Room: Stability and Medians (Joint with Flip Klijn, published in Social Choice and Welfare in 2010)
Abstract: We consider one-to-one, one-sided matching (roommate) problems in which agents can either be matched as pairs or remain single. We introduce a so-called bi-choice graph for each pair of stable matchings and characterize its structure. Exploiting this structure we obtain as a corollary the "lone wolf'' theorem and a decomposability result. The latter result together with transitivity of blocking leads to an elementary proof of the so-called stable median matching theorem, showing how the often incompatible concepts of stability (represented by the political economist Adam Smith) and fairness (represented by the political philosopher John Rawls) can be reconciled for roommate problems. Finally, we extend our results to two-sided matching problems.
Paper 2: Farsighted Stability for Roommate Markets (joint with Flip Klijn and Markus Walzl)
Abstract: We study farsighted stability for roommate markets. We show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter. Using this characterization of indirect dominance, we investigate von Neumann-Morgenstern farsightedly stable sets. We show that a singleton is von Neumann-Morgenstern farsightedly stable if and only if the matching is stable. We also present a roommate market without a von Neumann-Morgenstern farsightedly stable set and a roommate market with a non-singleton von Neumann-Morgenstern farsightedly stable set. |
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| responsibles | Chevaleyre |
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