Assignment markets with capacitated middlemen: core and competitive equilibria

Abstract We consider a three-sided market where each buyer-seller pair can attain a profit only if there is a middleman that connects them. This profit does not depend on the identity of the middlemen, and each buyer and seller can take part in at most one partnership while middlemen can establish multiple partnerships, up to their capacity. We show that the core is non-empty and strictly contains the set of competitive equilibrium payoff vectors that coincides with the set of solutions of the dual q -assignment problem, where q is the total capacity of the middlemen.