A Theory of Stability in Many-to-Many Matching Markets

We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and with the predictions of a non-cooperative bargaining model. The setwise-stable set possesses the 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.

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