Dynamic Matching: Shall we commit to not competing?

Appointments occur sequentially in various many-to-one matching markets such as college admissions and entry-level professional labor markets in the US. Although literature rations early matchings with a competition argument—that is, institutions compete to hire better agents early on—early matchings in some markets (e.g. job market for Finance Ph.D. candidates) show inferior quality. This paper introduces a suitable notion of dynamic group stability and shows that institutions can rationally benefit from committing to match worse early on. Such a commitment lowers the competition for better agents in the subsequent market.