We consider the problem of optimal information sharing in the context of a service system. In particular, we consider an unobservable single server queue offering service at a fixed price to a Poisson arrival of delay-sensitive customers. The service provider can observe the queue, and may share information about the state of the queue with each arriving customer. The customers are Bayesian and strategic, and incorporate any information provided by the service provider into their beliefs about the queue size before deciding whether to join the queue or leave without obtaining service. We pose the following question: which signaling mechanism should the service provider adopt to maximize her revenue? We establish that, in general, the optimal signaling mechanism requires the service provider to strategically conceal information from the customers to incentivize them to join. In particular, we show that a signaling mechanism with two signals and a threshold structure is optimal. Furthermore, for the case of linear waiting costs, we obtain analytical expressions for the thresholds of the optimal signaling mechanism. Finally, we prove that the optimal signaling mechanism under the optimal fixed price can achieve the revenue of the optimal state-dependent pricing mechanism. This suggests that in settings where state-dependent pricing is not feasible, the service provider can effectively use optimal signaling to achieve the optimal revenue. Our work contributes to the literature on Bayesian persuasion in dynamic settings, and provides many interesting directions for extensions (joint work with David Lingenbrink, Cornell University)).
