Optimal Signaling Mechanisms in Unobservable Queues

38 Pages Posted: 8 May 2017 Last revised: 22 Jul 2018

See all articles by David Lingenbrink

David Lingenbrink

Cornell University

Krishnamurthy Iyer

University of Minnesota - Twin Cities - Department of Industrial and Systems Engineering

Date Written: July 9, 2018

Abstract

We consider the problem of optimal information sharing in an unobservable single-server queue offering service at a fixed price to a Poisson arrival of delay-sensitive customers. The service provider observes the queue, and may share state information with arriving customers. The customers are Bayesian and strategic, and incorporate this information into their beliefs before deciding whether to join the queue. We pose the following question: which signaling mechanism should the service provider adopt to maximize her expected revenue? We formulate this problem as an infinite linear program in the queue's steady-state distribution, and establish that, in general, the optimal signaling mechanism requires the service provider to strategically conceal information in order to incentivize customers to join. In particular, we show that a binary signaling mechanism with a threshold structure is optimal. Finally, we prove that coupled with an optimal fixed price, the optimal signaling mechanism generates the same expected revenue as the optimal state-dependent pricing mechanism. This suggests that in settings where state-dependent pricing is infeasible, signaling can be effective in achieving the optimal revenue. Our work contributes to the literature on dynamic Bayesian persuasion, and provides many interesting directions for extensions.

Keywords: dynamic Bayesian persuasion, infinite linear program, threshold mechanism

JEL Classification: C72, D82

Suggested Citation

Lingenbrink, David and Iyer, Krishnamurthy, Optimal Signaling Mechanisms in Unobservable Queues (July 9, 2018). Available at SSRN: https://ssrn.com/abstract=2964093 or http://dx.doi.org/10.2139/ssrn.2964093

David Lingenbrink

Cornell University ( email )

Ithaca, NY 14853
United States

Krishnamurthy Iyer (Contact Author)

University of Minnesota - Twin Cities - Department of Industrial and Systems Engineering ( email )

111 Church St SE
Minneapolis, MN 55455
United States

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