On the Efficiency of Queueing in Dynamic Matching Markets

This paper considers a two-sided dynamic matching market where agents arrive at the market randomly. An arriving agent is immediately matched if there are agents waiting on the other side. Otherwise, the arriving agent has to decide whether to leave the market and take her outside option or to join a (possibly empty) queue and wait for a match. The equilibrium is characterized by a cutoff, k ∗ , so that an agent joins the queue if, and only if, the length of the queue is less than k ∗ . Our main result compares k ∗ with the socially optimal queue size, K ∗ . In particular, we show that if the arrival rate of the agents is (small) large then k ∗ ≥ (≤)K ∗ , that is, agents are too (im)patient. In addition, we characterize parameter values for which K ∗ = ∞