Discrete revealed preference and lattice of stable multipartner matchings
by
Ahmet Alkan
Sabanci University

In the original college admissions problem, each college had a strict ordering on the set of all of its acceptable applicants and a quota giving the maximum number it could admit. In a symmetric model of multipartner matching, with agents given by rather general choice functions and no quota restrictions, Blair (1988) proved that stable matchings always exist and form a lattice. He noted in particular, however, that the lattice operations need not be distributive. Recently Alkan (2000) showed that if one reintroduces quotas in a natural way, then the set of stable matchings is a distributive lattice, under a natural definition of least upper bound for pairs of matchings, and has a number of interesting structural properties. In this study we show that the quota restriction can be removed and replaced by a more general condition named "cardinal monotonicity" and all the properties still hold. We have in particular the somewhat surprising result that although there are no exogenous quotas in the model there is endogenously a sort of quota, namely, an agent has the same number of partners in every stable matching.

Date received: June 12, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafi-48.