We study matching policies in a dynamic exchange market with random compatibility, in which some agents are easier to match than others. In steady state this asymmetry creates an endogenous imbalance: hard-to-match agents wait for partners, while easy-to-match agents can match almost immediately upon arrival and leave the market quickly . A greedy policy, which attempts to match agents upon arrival, does not account for the positive externality  waiting agents generate as they make it easier to match agents that arrive in the future , and may result in more unmatched than other policies. While this trade-off between a "thickermarket" and quick matching is present in small markets we show that it vanishes in large markets and the greedy policy nevertheless dominates any other dynamic matching policy. As arrival rate increases the greedy policy matches a (weakly) higher fraction of agents than any other policy and leads to (weakly) lower average waiting time than any other policy. We show that in a large market greedy matching strictly outperforms batching policies (e.g., weekly matching) and a patient policy, which attempts to match agents only as they are about to depart the market. We test our large market predictions with kidney exchange data from the National Kidney Registry (NKR). Numerical simulations show that, in line with our predictions, the greedy policy matches patient-donor pairs significantly faster (roughly 20-30 days) than other commonly used policies and at most 1 \\%DIF < percent fewer pairs than the patient policy.\end{abstract} %DIF > more than monthly-batching), and shorter patient waiting times.
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 \\%DIF < percent fewer pairs than the patient policy.\end{abstract} %DIF > more than monthly-batching), and shorter patient waiting times.
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matching policies in a dynamic exchange market with random compatibility, in which some agents are easier to match than others. In steady state this asymmetry creates an endogenous imbalance:
dynamic matching in exchange markets with easy- and
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wait for partners, while easy-to-match agents can match almost immediately upon arrival and leave the market quickly
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does not account for
ignores
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that
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as they make it easier to match agents that arrive in the future , and may result in more unmatched than other policies. While
by facilitating future matchings. We prove that
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"thickermarket" and quick matching is present in small markets we show that it
``thicker'' market and faster matching
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and the greedy policy nevertheless dominates any other dynamic matching policy. As arrival rate increases the greedy policy matches a (weakly) higher fraction of agents than any other policy and leads to (weakly) lower average waiting time
; A greedy policy leads to shorter waiting times, and more agents matched
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show that in a large market greedy matching strictly outperforms batching policies (e.g., weekly matching) and a patient policy, which attempts to match agents only as they are about to depart the market. We test our large market predictions with kidney exchange
empirically confirm these findings in
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(NKR). Numerical simulations show that, in line with our predictions, the greedy policy matches patient-donor pairs significantly faster (roughly 20-30 days) than other commonly used policies and at most 1
. Greedy matching achieves as many transplants as commonly-used policies (1.6