Robert Shimer from the University of Chicago will present "Assortative Matching with Private Information"

Abstract: We study matching markets with two-sided private information where agents care about their partner’s unobserved type. Competing platforms post fees and promised partner distributions, while privately-informed agents direct their search to preferred platforms. Under common ranking and supermodularity, we prove that equilibrium must be separating: each platform attracts exactly one type from each side. We characterize positive assortative matching equilibria and provide sufficient conditions for their existence. The mechanism for separation depends crucially on willingness-to-pay: when more desirable types have higher willingness-to-pay for any match, they separate through high fees; when they have lower willingness-to-pay, they separate through low matching rates.