Optimal Signaling Mechanisms in Unobservable Queues

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)

Krishnamurthy Iyer is an Assistant Professor in the School of
Operations Research and Information Engineering at Cornell
University. He received his PhD from the Department of Management
Science and Engineering at Stanford University in 2012, and his B.Tech
and M.Tech (dual degree) in Mechanical Engineering at the Indian
Institute of Technology, Bombay in 2006. Before coming to Cornell, he
was a Postdoctoral Researcher at the Computer and Information Science
Department in the University of Pennsylvania. His research interests
include game theory, stochastic modeling, dynamic markets, and mean
field models.