Abstract: We consider centralized dynamic matching markets with finitely many agent types and heterogeneous match values. A network topology determines the feasible matches in the market and the value generated from each match. An inherent trade-off arises between short- and long-term objectives. A social planner may delay match decisions to thicken the market and increase match opportunities to generate high value. This inevitably compromises short-term value, and the planner may match greedily to maximize short-term objectives.