On the invariance of the set of Core matchings with respect to preference profiles

We consider the general many-to-one matching model with ordinal preferences and give a procedure to partition the set of preference pro…les into subsets with the property that all preference pro…les in the same subset have the same Core. We also show how to identify a pro…le of (incomplete) binary relations containing the minimal information needed to generate as strict extensions all the (complete) preference pro…les with the same Core. This is important for applications since it reduces the amount of information that agents have to reveal about their preference relations to centralized Core matching mechanisms; moreover, this reduction is maximal. Keywords: Matching, Core. Journal of Economic Literature Classi…cation Number: C78. We are very grateful to Flip Klijn for his helpful comments. We also thank members of the Bag Lunch Workshop on Game Theory and Social Choice at Universitat Autònoma de Barcelona for comments and suggestions. 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 Cientí…cas y Técnicas through grant PICT-02114. 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 the Barcelona Graduate School of Economics, where he is an a¢ liated professor, through its Research Recognition Programme. 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. yInstituto de Matemática Aplicada de San Luis. Universidad Nacional de San Luis and CONICET. Ejército de los Andes 950. 5700, San Luis, Argentina. E-mails: [email protected], [email protected], and [email protected] zDepartament d’Economia i d’Història Econòmica and CODE. Universitat Autònoma de Barcelona. 08193, Bellaterra (Barcelona), Spain. E-mail: [email protected]