We introduce a simple model of dynamic matching in networked markets, where agents arrive and depart stochastically and the composition of the trade network depends endogenously on the matching algorithm. If the planner can identify agents who are about to depart, then waiting to thicken the market substantially reduces the fraction of unmatched agents. If not, then matching agents greedily is close to optimal. We specify conditions under which local algorithms that choose the right time to match agents, but do not exploit the global network structure, are close to optimal. Finally, we consider a setting where agents have private information about their departure times and design a mechanism to elicit this information.
