We consider a canonical revenue management (RM) problem wherein a monopolist seller posts prices for multiple products that are for sale over a fixed horizon so as to maximize expected revenues. Products are differentiated and subject to joint capacity constraints. Arriving 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 has established that static prices are asymptotically optimal for this problem in the regime where inventory and demand grow large. In stark contrast, for the case where customers are forward looking, available results in mechanism design and dynamic pricing suggest substantially more complicated prescriptions. Notably, these results apply to settings with merely a single product type, and they are also often constrained by restrictive assumptions on customer type. We demonstrate that static prices surprisingly remain asymptotically optimal in the face of strategic customers for a multiproduct setting and for a broad class of customer utility models. For the single-product case, we further show that an optimally set static price guarantees the seller revenues that are within at least 63.2% of that under an optimal dynamic pricing policy, irrespective of regime. For utility models outside the class we consider, we show that static prices need not be asymptotically optimal. Nevertheless, the class of customer utility models we consider is parsimonious, enjoys empirical support, and subsumes many of the models considered for this problem in existing mechanism design research. We allow for multidimensional customer types and for a customer’s disutility from waiting to be positively correlated with his valuation. Therefore, our findings are likely to be robust and provide for a canonical RM problem a simple prescription that is near-optimal across a broad set of modeling assumptions. This paper was accepted by Yinyu Ye, optimization.
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