Stable Matching with Peer-Dependent Preferences in Large Markets: Existence and Cutoff Characterization

Abstract

This paper studies two-sided many-to-one matching in which student preferences can depend on the assignment of other students, allowing for peer effects and externalities. We show that stable matchings are tractably described by cutoffs and matching statistics that satisfy a market clearing and rational expectations condition. A diversity of preferences assumption guarantees existence of a stable matching in the continuum model. This assumption allows discontinuous student preferences, but requires that a small change to the assignment makes a small fraction of students change their ordinal rankings over colleges. Using this result, we show existence of an approximately stable matching in finite sampled economies.