Annals of Operations Research

This paper studies matching markets in the presence of middlemen. In our framework, a buyer-seller pair may either trade directly or use the services of a middleman; and a middleman may serve multiple buyer-seller pairs. For each such market, we examine the associated TU game. We first show that, in our context, an optimal matching can be obtained by considering the two-sided assignment market where each buyer-seller pair is allowed to use the mediation services of any middleman free of charge. Second, we prove that matching markets with middlemen are totally balanced: in particular, we show the existence of a buyer-optimal (seller-optimal) core allocation where each buyer (seller) receives her marginal contribution to the grand coalition. In general, the core does not exhibit a middleman-optimal allocation, not even when there are only two buyers and two sellers. However, we prove that in these small markets the maximum core payoff to each middleman is her marginal contribution. Finally, we establish the coincidence between the core and the set of competitive equilibrium payoff vectors. Hungarian National Research,Development and Innovation Office [NKFIH K-119930] Published version Ata Atay is a Serra Hunter Fellow (Professor Lector Serra Hunter) under the Serra Hunter Plan (Pla SerraHunter). Any opinions, findings, interpretations, conclusions or recommendations expressed in this paper arethose of its authors and do not necessarily reflect the views of the National Science Foundation. Ata Ataygratefully acknowledges financial support from the University of Barcelona through Grant AS017672.Tamas Solymosi gratefully acknowledges financial support from the Hungarian National Research,Development and Innovation Office through Grant NKFIH K-119930.