Dynamic Many-to-One Matching

We study many-to-one matching markets in a dynamic framework with the following features: Matching is irreversible, participants exogenously join the market over time, each agent is restricted by a quota, and agents are perfectly patient. A form of strategic behavior in such markets emerges: The side with many slots can manipulate the subsequent matching market in their favor via earlier matchings. In such a setting, a natural question arises: Can we analyze a dynamic many-to-one matching market as if it were either a static many-to-one or a dynamic one-to-one market? First, we provide sufficient conditions under which the answer is yes. Second, we showthat if these conditions are not met, then the early matchings are “inferior” to the subsequent matchings. Lastly, we extend the model to allow agents on one side to endogenously decide when to join the market. Using this extension,we provide a rationale for the small amount of unraveling observed in the US medical residency matching market compared to the US college-admissions system