Nicole Immorlica, Jacob D. Leshno, Irene Lo, Brendan Lucier
We explore the acquisition and flow of information in matching markets through a model of college admissions with endogenous costly information acquisition. We extend the notion of stability to this partial information setting, and introduce regret-free stability as a refinement that additionally requires optimal student information acquisition. We show regret-free stable outcomes exist, and finding them is equivalent to finding appropriately-defined market-clearing cutoffs. To understand information flows, we recast matching mechanisms as price-discovery processes. No mechanism guarantees a regret-free stable outcome, because information deadlocks imply some students must acquire information sub optimally. Our analysis suggests approaches for facilitating efficient price discovery, leveraging historical information or market sub-samples to estimate cutoffs. We show that mechanisms that use such methods to advise applicants on their admission chances yield approximately regret-free stable outcomes. A survey of university admission systems highlights the practical importance of providing applicants with information about their admission chances.
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