  This paper develops a framework for repeated matching markets. The model
departs from the Gale-Shapley matching model by having a fixed set of
long-lived hospitals match with a new generation of short-lived residents in
every period. I show that there are two kinds of hospitals in this repeated
environment: some hospitals can be motivated dynamically to voluntarily reduce
their hiring capacity, potentially making more residents available to rural
hospitals; the others, however, are untouchable even with repeated interaction
and must obtain the same match as they do in a static matching. In large
matching markets with correlated preferences, at most a vanishingly small
fraction of the hospitals are untouchable. The vast majority of hospitals can
be motivated using dynamic incentives.
