Equilibrium in Queues under Unknown Service Rates and Service Value

We study a single queue joining equilibrium when there is uncertainty in the consumers’ minds about the service rate and value. Without such uncertainty, the joining equilibria are characterized by means of a single threshold queue length above which consumers do not join (Naor, 1969). We show that in the presence of such uncertainty, the equilibrium joining strategy is not fully characterized by a single threshold. A “sputtering equilibrium” might exist. In the sputtering equilibrium, the queue length generally remains within a threshold, but reaches another, strictly higher, threshold, depending on the outcome of the randomized decision of the consumer arriving at the lower threshold. We discuss when and why sputtering equilibria exist.