Abstract. We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwisestable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwisestable set coincides with the pairwise-stable set, and with the predictions of a non-cooperative bargaining model. The set-wise stable set possesses the canonical conflict/coincidence of interest properties from many-to-one, and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core-like solutions, besides the setwise-stable set.
Echenique et al REF study several solution concepts, such as the setwise-stable set, the core, and the bargaining set in many-to-many matchings.
A Theory of Stability in Many-to-Many Matching Markets
Theoretical Economics, Society for Economic Theory
Mathematics