Optimal dynamic matching

We study a dynamic matching environment where individuals arrive sequentially. There is a trade-off between waiting for a thicker market, allowing for higher-quality matches, and minimizing agents' waiting costs. The optimal mechanism cumulates a stock of incongruent pairs up to a threshold and matches all others in an assortative fashion instantaneously. In discretionary settings, a similar protocol ensues in equilibrium, but expected queues are inefficiently long. We quantify the welfare gain from centralization, which can be substantial, even for low waiting costs. We also evaluate welfare improvements generated by alternative priority protocols.