Stable matching mechanisms are used to clear many two-sided markets. In practice, these mechanisms leave many agents on both sides unmatched. What factors determine the number of unmatched agents, and the quality of matches that do form? This paper answers this question, with a particular focus...

We study a setting in which dynamically arriving items are assigned to waiting agents, who have heterogeneous values for distinct items and heterogeneous outside options. An ideal match would both target items to agents with the worst outside options, and match them to items for which they have...