Existence and Testable Implications of Extreme Stable Matchings

We investigate the testable implications of the theory that markets produce matchings that are optimal for one side of the market; i.e. stable extremal matchings. A leading justification for the theory is that markets proceed as if the deferred acceptance algorithm were in place. We find that the theory of stable extremal matching is observationally equivalent to requiring that there be a unique matching, or that the matching be consistent with unrestricted monetary transfers. We also present results on rationalizing a matching as the median stable matching. We work with a general model of matching, which encompasses aggregate and random matchings as special cases. As a consequence, we need to work with a notion of strong stability, and extend the standard theory on the existence and structure of extremal matchings