Interview Assignment Mechanisms, Stability and Incentives

In recent years, in the markets for residency and fellowship positions at hospitals in the US, many market participants have expressed discontent with the process through which interviews are determined. In this paper, I show that matching with interviews is a special case of matching with externalities in which agents' preferences need not be substitutable: agents care not only about whom they are interviewing, but also about whom others are interviewing, and agents may want to interview someone only if certain other interviews are available to them. To address the inadequacy of the classical formulations of stability, I propose an alternative formulation of stability in interview markets, and I characterize the set of stable interview assignments for special cases analyzed in the literature. I also analyze the properties of the deferred-acceptance interview assignment mechanisms and show that it fails at high rates to reach stable interview assignments even under truthful reporting by agents. Moreover, this mechanisms generally does not make it a dominant strategy for either side of the market to report their preferences truthfully. Unlike in the classical matching models, an agent's incentives to misreport their preferences depend not only on the agent's own interview quota, but also on the interview quotas on the opposite side of the market