On the revealed preference analysis of stable aggregate matchings

Echenique, Lee, Shum, and Yenmez (2013) established the testable revealed preference restrictions for stable aggregate matching with transferable and nontransferable utility and for extremal stable matchings. In this paper, we rephrase their restrictions in terms of properties on a corresponding bipartite graph. From this, we obtain a simple condition that verifies whether a given aggregate matching is rationalizable. For matchings that are not rationalizable, we provide a simple greedy algorithm that computes the minimum number of matches that need to be removed to obtain a rationalizable matching. We also show that the related problem of finding the minimum number of types that we need to remove in order to obtain a rationalizable matching is NP-complete.