Many-to-Many Matching and Price Discrimination⇤

We study centralized many-to-many matching in markets where agents have private informa-tion about (vertical) characteristics that determine match values. Our analysis reveals how match-ing patterns reflect cross-subsidization between sides. Agents are endogenously partitioned into consumers and inputs. At the optimum, the costs of procuring agents-inputs are compensated by the gains from agents-consumers. We show how such cross-subsidization can be achieved through matching rules that have a simple threshold structure and are assortative in the weak-order (set inclusion) sense. We then deliver testable predictions relating the optimal matching rules and price schedules to the distribution of the agents ’ characteristics. The analysis has implications for the design of large matching intermediaries, such as advertising exchanges, business-to-business platforms, and online job-matching agencies. JEL classification: D8