We study the problem of optimal information sharing in the context of a service system. In particular, we consider an unobservable single server queue o ering a service at a xed price to a Poisson arrival of delaysensitive customers. e service provider can observe the queue, and may share information about the state of the queue with each arriving customer. e customers are Bayesian and strategic, and incorporate any information provided by the service provider into their prior beliefs about the queue length before making the decision whether to join the queue or leave without obtaining service. We pose the following question: which signaling mechanism and what price should the service provider select to maximize her revenue? We formulate this problem as an instance of Bayesian persuasion in dynamic se ings. e underlying dynamics make the problem more di cult because, in contrast to static se ings, the signaling mechanism adopted by the service provider a ects the customers' prior beliefs about the queue (given by the steady state distribution of the queue length in equilibrium). e core contribution of this work is in characterizing the structure of the optimal signaling mechanism. We summarize our main results as follows. (1) Structural characterization: Using a revelation-principle style argument, we nd that it su ces to consider signaling mechanisms where the service provider sends a binary signal of "join" or "leave", and under which the equilibrium strategy of a customer is to follow the service provider's recommended action. (2) Optimality of threshold policies: For a given xed price for service, we use the structural characterization to show that the optimal signaling mechanism can be obtained as a solution to a linear program with a countable number of variables and constraints. Under some mild technical conditions on the waiting costs, we establish that there exists an optimal signaling mechanism with a threshold structure, where service provider sends the "join" signal if the queue length is below a threshold, and "leave" otherwise. (In addition, at the threshold, the service provider randomizes.) For the special case of linear waiting costs, we derive an analytical expression for the optimal threshold in terms of the two branches of the Lambert-W function. (3) Revenue comparison: Finally, we show that with the optimal choice of the xed price and using the corresponding optimal signaling mechanism, the service provider can achieve the same revenue as with the optimal state-dependent pricing mechanism in a fully-observable queue. is implies that in se ings where state-dependent pricing is not feasible, the service provider can e ectively use optimal signaling (with the optimal xed price) to achieve the same revenue.
In the setting of strategic delay announcements for queueing, REF show that when the principal is a revenue maximizer, a binary signaling mechanism with a threshold structure is optimal.