On the invariance of the set of stable matchings with respect to substitutable preference profiles

Abstract

We are very grateful to José Alcalde, Guillaume Haeringer, Flip Klijn, Joana Pais, and two anonymous referees for their 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, by the Consejo Nacional de Investigaciones Científicas y Técnicas CONICET through grant PICT-02114, and by the Agencia Nacional de Promoción Científica y Técnica through grants 03-10814 and PAV-008. The work of J. Massó is partially supported by the Ministerio de Educación y Ciencia (Spain), through grant SEJ2005-01481/ECON and FEDER and project CONSOLIDER-INGENIO 2010 (CDS2006-00016), and by the Generalitat de Catalunya through grant SGR2005-00454 and through the Barcelona Economics Program (XREA). All authors acknowledge financial support from the grants PCI España-Iberoamérica 2005 and 2006 (Programa de Cooperación Interuniversitaria de la Agencia Española de Cooperación Internacional-AECI).

Altres ajuts: PICT-02114

Altres ajuts: SEJ2005-01481

For the many-to-one matching model we give a procedure to partition the set of substitutable preference profiles into equivalence classes with the property that all profiles in the same class have the same set of stable matchings. This partition allows to reduce the amount of information required by centralized stable mechanisms.