Inferring Quality from a Queue

In this paper, we study how rational agents infer the quality of a good (a product or a service) by observing the queue that is formed by other rational agents to obtain the good. Agents also observe privately the realization of a signal that is imperfectly correlated with the true quality of the good. Based on the queue length information and the signal realization, agents decide whether to join the queue and obtain the good or to balk. The time to produce the good is exponentially distributed. Agents arrive according to a Poisson process at a market and are served according to a FIFO discipline. We find that when waiting costs are zero, agents receiving a bad signal join the queue only if it is long enough. When waiting costs are strictly positive, agents do not join the queue if it is too long. Furthermore, there may exist a set of isolated queue lengths (“holes”) at which agents with a bad signal do not join. In equilibrium, queues are shorter for low quality goods and an agent is more likely to erroneously join a queue for a low quality good than erroneously balk from a queue for a high quality good. When decreasing the service rate, more agents may join queues for high quality goods, even when waiting is costly