Random matching in the college admissions problem - Pais, Joana (2022)
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 equilibria. Namely, every ordinal equilibrium yields a degenerate probability distribution. Furthermore, individual rationality is a necessary and sufficient condition for an equilibrium outcome, while stability is guaranteed in ordinal equilibria where firms act straightforwardly. Finally, we relate equilibrium behavior in random and in deterministic mechanisms.