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 on how match outcomes depend on correlations in agent preferences. I consider three canonical preference structures: fully idiosyncratic preferences, common preferences (agents agree on the attractiveness of those on the opposite side), and aligned preferences (potential partners agree on the attractiveness of their match).
I find that idiosyncratic preferences result in more matches than common preferences do. Perhaps more surprisingly, the case of aligned preferences results in the fewest matches. Regarding match quality, the story reverses itself: aligned preferences produce the most high quality matches, followed by common preferences. These facts have implications for the design of priority rules and tie-breaking procedures in school choice settings, as they point to a fundamental tradeoff between matching many students, and maximizing the number of students who get one of their top choices.
Arnosti, Nicholas. "Centralized Clearinghouse Design: A Quantity-Quality Tradeoff." Columbia Business School, January 2016.
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