On the efficiency of queueing in dynamic matching markets

We study a two-sided dynamic matching market where agents arrive randomly. An arriving agent is immediately matched if agents are waiting on the other side. Otherwise, the agent decides whether to exit the market or join a queue to wait for a match. Waiting is costly: agents discount the future and incur costs while they wait. We characterize the equilibrium and socially optimal queue sizes under first-come, first-served. Depending on the model parameters, equilibrium queues can be shorter or longer than efficiency would require them to be. Indeed, socially optimal queues may be unbounded, even if equilibrium queues are not. By contrast, when agents only incur flow costs while they wait, equilibrium queues are typically longer than socially optimal ones (cf. Baccara et al., 2020). Unlike one-sided markets, the comparison between equilibrium and socially optimal queues in two-sided markets depends on agents' time preferences.