An Algorithm To Compute The Set Of Many-To-Many Stable Matchings

The paper proposes an algorithm to compute the set of many-to-many stable matchings when agents have substitutable preferences. The algorithm starts by calculating the two optimal-stable matchings using the deferred-acceptance algorithm. Then, it computes each remaining stable matching as the firm-optimal stable matching corresponding to a new preference profile which is obtained after modifying the preferences of a previously identified sequence of firms.Financial support through a grant from the Programa de Cooperación Científica Iberoamericana is acknowledged. The work of J. 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.Peer reviewe