  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. Direct
trade between a buyer and a seller is costlier than a trade mediated by a
middleman. For each such market, we examine an associated cooperative game with
transferable utility. First, we show that an optimal matching for a matching
market with middlemen can be obtained by considering the two-sided assignment
market where each buyer-seller pair is allowed to use the mediation service of
the middlemen free of charge and attain the maximum surplus. Second, we prove
that the core of a matching market with middlemen is always non-empty. Third,
we show the existence of a buyer-optimal core allocation and a seller-optimal
core allocation. In general, the core does not exhibit a middleman-optimal
matching. Finally, we establish the coincidence between the core and the set of
competitive equilibrium payoff vectors.
