How does the design of a marketplace affect the flow and acquisition of information in the market? We explore this question in a model of college admissions that formally accounts for students' information acquisition costs in forming their preferences. In this model students may rationally choose to remain partially informed, and we extend the notion of stability to this partial information setting. Our main question is whether the market can reach a stable outcome while facilitating efficient information acquisition by all students. To address this question, we define a regret-free stable outcome as a benchmark for efficient information acquisition.
We show that regret-free stable outcomes always exist, and are characterized by market-clearing cutoffs. Standard matching mechanisms can be seen as asking students to engage in price-discovery to discover these cutoffs, and this price-discovery process can be costly. Instead, we emphasize the usefulness of additional sources of information. We show that estimating cutoffs from historical market information allows for an approximately optimal outcome, and provide a procedure for bootstrapping cutoffs when historical market information is not available. Our results suggest that given sufficient information, matching markets can perform well even with simple or decentralized mechanisms.
This is joint work with Nicole Immorlica, Jacob Leshno, and Brendan Lucier.