Efficient Interview Scheduling for Stable Matching
The study of stable matchings usually relies on the assumption that agents' preferences over the opposite side are complete and known. In many real markets, however, preferences might be uncertain and revealed only through costly interactions such as interviews. We show how to reach interim-stable matchings, under which all matched pairs must have interviewed and agents use expected utilities whenever true values remain unknown, while minimizing both the expected number of interviews and the expected number of interview rounds. We introduce two adaptive algorithms that produce interim-stable matchings: one operates sequentially, and another is a hybrid algorithm that begins by scheduling some interviews in parallel and continues sequentially. Focusing on cases where agents are ex-ante indifferent between agents on the other side, we show that the sequential algorithm performs 2 interviews per agent in expectation. We complement this by showing that any algorithm that performs less than 2 interviews per agent, does not always guarantee interim-stability. We also demonstrate that the hybrid algorithm requires only polylogarithmic expected number of rounds, while still performing only about 2 interviews per agent in expectation. Additionally, the interviews scheduled by our algorithms guarantee an interim-stable matching when Deferred-Acceptance is run after all interviews are completed.