Many-to-One Matching with Transfers

About this event

We study many-to-one matching with transfers and peer effects. The setting generalizes both assignment models (optimal transport) and Bayesian persuasion. Equilibrium exists and is efficient under general conditions. We give necessary and sufficient conditions for positive segregation, where workers are segregated and matched to firms in a positively assortative manner. When peer effects are linear (mean-measurable) and worker and firm types have the same distribution, positive segregation holds if and only if the ratio of the cross-partial between (mean) worker and firm type and the second-partial with respect to worker type---which we call the marginal marginal rate of substitution (MMRS)---exceeds 1. When this condition fails, equilibrium features alternating intervals of segregation and compression (incomplete pooling). Equilibrium is more segregated when the MMRS is higher and workers are more heterogeneous. When peer effects are unpriced (as in models of neighborhood or school choice), we characterize when equilibrium is excessively segregated.