["The RAND Journal of Economics, EarlyView. ", "\nABSTRACT\nA 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 stochastically negative assortative when there are few low‐value buyers (i.e., compared to lower‐quality sellers, high‐quality ones are matched to buyers with lower expected valuation). Although everyone trades, generating rents for the side lacking bargaining power results in inefficient matching."]