Deadlines and matching

Abstract

Deadlines and fixed end dates are pervasive in matching markets. Deadlines drive fundamental non-stationarity and complexity in behavior, generating significant departures from the steady-state equilibria usually studied in the search and matching literature. I consider a two-sided matching market with search frictions where vertically differentiated agents attempt to form bilateral matches before a deadline. I give novel proofs of existence and uniqueness of equilibria, and show that all equilibria exhibit an “anticipation effect” where less attractive agents become increasingly choosy over time, preferring to wait for the opportunity to match with attractive agents who, in turn, become less selective as the deadline approaches. When agents are patient, a sharp characterization is available: at any point in time, the market segments into a first class of matching agents and a second class of waiting agents. This points to a different interpretation of unraveling.