Kadam, Sangram V., and Maciej H. Kotowski. "Multiperiod Matching." International Economic Review 59.4 (November 2018): 1927-1947.

Abstract

We examine a dynamic, two-sided, one-to-one matching market where agents on both sides interact over a period of time. We define and identify sufficient conditions for the existence of a dynamically stable matching, which may require revisions to initial assignments. A generalization of the deferred acceptance algorithm can identify dynamically stable outcomes in a large class of economies, including cases with intertemporal preference complementarities. We relate our analysis to market unraveling and to common market design applications, including the medical residency match.