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We study many-to-one matching with transfers and peer effects, such as matching workers to firms, students to schools, residents to neighborhoods, or consumers to status goods. The setting generalizes both assignment models (optimal transport) and Bayesian persuasion. Equilibrium exists and is efficient under general conditions. We give a simple necessary and sufficient condition for positive segregation, where workers are segregated and matched to firms in a positively assortative manner. When this condition fails, equilibrium features alternating intervals of segregation and compression. Comparative statics characterize when equilibrium is more segregated or more compressed. When peer effects are unpriced (as in school or neighborhood choice), we characterize when equilibrium is excessively segregated.
