Dynamic Many-to-One Matching

Abstract. We study the stability on many-to-one matching markets in a dynamic framework with the following features: matching is irreversible, participants -exogenously- join market over time, and each agent on one side 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 show that if these conditions are not met, then the early matchings are inferior compared 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 little unraveling observed in the US medical residency matching market compared to the US college admissions system.