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Matching in Dynamic Imbalanced Markets

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 Added by Itai Ashlagi
 Publication date 2018
  fields Economy
and research's language is English




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We study dynamic matching in exchange markets with easy- and hard-to-match agents. A greedy policy, which attempts to match agents upon arrival, ignores the positive externality that waiting agents generate by facilitating future matchings. We prove that this trade-off between a ``thicker market and faster matching vanishes in large markets; A greedy policy leads to shorter waiting times, and more agents matched than any other policy. We empirically confirm these findings in data from the National Kidney Registry. Greedy matching achieves as many transplants as commonly-used policies (1.6% more than monthly-batching), and shorter patient waiting times.



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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.
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