On the lattice structure of the set of stable matchings for a many-to-one model

We thank José Alcade, Howard Petith, Alvin Roth, and a referee for their helpful comments. Financial support through a grant from the Programa de Cooperación Científica Iberoamericana is acknowledged. The work of Jordi Massó is also partially supported by Research Grants PB98-0870 from the Dirección General de Investigación Científica y Técnica, Spanish Ministry of Education and Culture, and SGR98-62 from the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. The paper was partially written while Alejandro Neme was visiting the UAB under a sabbatical fellowship from the Spanish Ministry of Education and CultureFor the many-to-one matching model with firms having substitutable and q-separable preferences we propose two very natural binary operations that together with the unanimous partial ordering of the workers endow the set of stable matchings with a lattice structure. We also exhibit examples in which, under this restricted domain of firms' preferences, the classical binary operations may not even be matchin