Random Matching in the College Admissions Problem

In the college admissions problem, we consider the incentives confronting agents who face the prospect of being matched by a random stable mechanism. We provide a fairly complete characterization of ordinal equilbria. Namely, every ordinal equilib- rium yields a degenerate probability distribution. Furthermore, individual rationality is a necessary and sufficient condition for an equilibrium outcome, while stability is guaranteed in ordinal equilibrium where firms act straightforwardly. Finally, we re- late equilibrium behavior in random and in deterministic mechanisms.