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.

中文翻译：

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在可转让效用下与中间商匹配市场

本文研究了在中间商存在的情况下匹配市场。在我们的框架中，买卖双方可以直接交易或使用中间人的服务；一个中间人可能会为多个买卖双方提供服务。买方和卖方之间的直接交易比由中间人调解的交易成本更高。对于每个这样的市场，我们研究了具有可转移效用的相关合作博弈。首先，我们证明了通过考虑允许每个买卖双方免费使用中间商的中介服务并获得最大剩余的双边转让市场，可以获得与中间商匹配市场的最优匹配。其次，我们证明了与中间商匹配的市场的核心始终是非空的。第三，我们展示了买方最优核心分配和卖方最优核心分配的存在。通常，核心不表现出中间人最优匹配。最后，我们建立了核心和竞争均衡支付向量集之间的重合。