Equilibrium in Queues Under Unknown Service Rates and Service Value

Abstract

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.

Keywords: Queueing games, Markov Perfect Bayesian Equilibrium, Threshold policies