Stability in Repeated Matching Markets

I develop a framework for studying repeated matching markets, where in every period, a new generation of short-lived agents on one side of the market is matched to a fixed set of long-lived institutions on the other. Within this framework, I characterize self-enforcing arrangements for two types of environments. When wages are rigid, as in the matching market for hospitals and medical residents, players can be partitioned into two sets: regardless of patience level, some players can be assigned only according to a static stable matching; when institutions are patient, the other players can be assigned in ways that are unstable in one-shot interactions. I discuss these results’ implications for allocating residents to rural hospitals. When wages can be flexibly adjusted, I show that with flexible wages, repeated interaction resolves well-known non-existence issues: while static stable matchings may fail to exist with complementarities and/or peer effects, self-enforcing matching processes always exist if institutions are sufficiently patient.