A platform matches a unit-mass of sellers, each owning a single product of heterogeneous
quality, to a unit-mass of buyers with differing valuations for unit-quality. After matching, sellers make take-it-or-leave-it price-offers to buyers. Initially, valuations of buyers are
only known to them and the platform, but sellers make inferences from the matching algorithm. The efficient matching is positive-assortative, but buyer-optimal matchings are, often,
stochastically negative-assortative (i.e., compared to lower-quality sellers, high-quality ones
are matched to buyers with lower expected valuation). Albeit everyone trades, generating
rents for the side lacking bargaining power results in inefficient matching.