Signaling Service Quality via Queue Disclosure

In this paper, we consider a single-server queuing system whose service quality is either high or low. The server, who knows the actual quality level, can signal such quality information to customers via revealing or concealing his queue length. Based on this and the observed queue length in the case of a revealed queue, customers decide whether or not to join. A non-cooperative game is hence formed, and we adopt the sequential equilibrium concept to solve this signaling game and apply the perfect sequential equilibrium as an equilibrium-refinement criterion. We first consider a general scenario in which the market is composed of both quality informed and uninformed customers. Under such a setting, when the server conceals his queue, we can fully characterize customers' equilibrium strategy and the corresponding effective arrival rate. The equilibrium outcome is a pooling strategy when the market size (measured by the potential arrival rate) is either below a lower threshold or above an upper threshold. Under the former, both high- and low-quality servers adopt queue concealment while under the latter, both types of servers adopt queue revelation. The separating equilibria exist only when the market size falls between these two thresholds, under which uninformed customers can infer the server's quality type based on his queue disclosure behavior. We further show that when customers are all uninformed of service quality, the equilibrium outcome is always a pooling one except at several discrete values of the market size