The Blocking Lemma for a many-to-one maching model
Martínez, Ruth (Universidad Nacional de San Luis (Argentina))
Neme, Alejandro (Universidad Nacional de San Luis (Argentina))
Massó, Jordi (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)
Oviedo, Jorge (Universidad Nacional de San Luis (Argentina))

Date:	2010
Abstract:	The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms' preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.
Grants:	Ministerio de Ciencia e Innovación ECO2008-04756 Ministerio de Ciencia e Innovación CDS2006-00016
Note:	We are grateful to Flip Klijn, Howard Petith, William Thomson, an associate editor, and two referees for very helpful comments. The work of R. Martínez, A. Neme and J. Oviedo is partially supported by the Universidad Nacional de San Luis, through grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas CONICET, through grant PIP 112-200801-00655. Support for the research of J. Massó was received through the prize "ICREA Acadèmia" for excellence in research, funded by the Generalitat de Catalunya. He also acknowledges the support of MOVE, where he is an affiliated researcher, and of the Barcelona Graduate School of Economics (through its Research Recognition Programme), where he is an affiliated professor. His work is also supported by the Spanish Ministry of Science and Innovation, through grants ECO2008-04756 (Grupo Consolidado-C) and CONSOLIDER-INGENIO 2010 (CDS2006-00016), and by the Generalitat de Catalunya, through grant SGR2009-419. All authors acknowledge financial support from an AECI grant from the Spanish Ministry of Foreign Affairs.
Note:	Altres ajuts: UNSL/319502
Note:	Altres ajuts: CONICET/PIP112-200801-00655
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió sotmesa a revisió
Subject:	Acoblament, Teoria de l' ; Matching ; Stability ; Blocking Lemma
Published in:	Journal of mathematical economics, Vol. 46 Núm. 5 (September 2010) , p. 937-949, ISSN 0304-4068

DOI: 10.1016/j.jmateco.2010.08.010

Preprint 27 p, 257.0 KB

The record appears in these collections:
Articles > Research articles
Articles > Published articles