This paper studies interdependent values in a matching market and how market participants strategically adjust to this situation. We study these questions in the market for medical school programs in Denmark, which assigns students to programs based on a centralized assignment mechanism. Using administrative data on student preferences, college priorities, and student outcomes, together with an information experiment, we present evidence that students and rival programs hold payoff relevant information that would, if known by the program, allow the program to admit students with lower program dropout rates. Building on these insights, we estimate an empirical model of this matching market that allows for heterogeneous program and student preferences as well as two sources of interdependent values: student self-selection and interdependent program values. Our findings suggest that both sources play a role and that programs benefit from learning information rival programs hold as well as learning about student preferences in identifying students with higher completion rates.