On the Efficacy of Static Prices for Revenue Management in the Face of Strategic Customers

TLDR: It is demonstrated that for a broad class of customer utility models, static prices surprisingly continue to remain asymptotically optimal in the scaling regime where inventory and demand grow large.

Abstract: The present paper considers a canonical revenue management problem wherein a monopolist seller seeks to maximize revenues from selling a fixed inventory of a product to customers who arrive over time. We assume that customers are forward looking and strategize on the timing of their purchase, an empirically confirmed aspect of modern customer behavior. In the event that customers were myopic, foundational work by Gallego and van Ryzin [1994] established that static prices were asymptotically optimal for this problem. In stark contrast, for the case where customers are forward looking, available results in mechanism design and dynamic pricing offer no such simple solution and are also constrained by restrictive assumptions on customer type. The present paper studies the revenue management problem while assuming forward looking customers. We demonstrate that for a broad class of customer utility models, static prices surprisingly continue to remain asymptotically optimal in the scaling regime where inventory and demand grow large. We further show that irrespective of regime, an optimally set static price guarantees the seller revenues that are within at least 63.2% of that under an optimal dynamic mechanism. The class of customer utility models we consider is parsimonious and enjoys empirical support. It also subsumes many of the utility models considered for this problem in existing mechanism design research; we allow for multi-dimensional customer types. We also allow for a customer's disutility from waiting to be positively correlated with his valuation. Our conclusions are thus robust and provide a simple solution to what is considered a challenging problem of dynamic mechanism design.