Multiproduct Dynamic Pricing with Limited Inventories Under a Cascade Click Model

Abstract

Problem definition: Designing effective operational strategies requires a good understanding of customer behavior. The classic economic theory of customer choice has long been the paradigm in the operations literature. However, the rise of online marketplaces such as e-commerce has triggered considerable efforts in academia and industry to develop alternative models that not only provide a good approximation of customer behavior but also are easily scalable for large-scale implementations. In this paper, we consider a multiproduct dynamic pricing problem with limited inventories under the so-called cascade click model, which is one of the most popular click models used in practice and has been intensively studied in the computer science literature. Methodology/results: We present some fundamental results. First, we derive a sufficiently general characterization of the optimal pricing policy and show that it has a different structure than the optimal policy under the standard pricing model. Second, we show that the optimal expected total revenue under the cascade click model can be upper bounded by the objective value of an approximate deterministic pricing problem. Third, we show that two policies that are known to have strong performance guarantees in the standard revenue management setting can be properly adapted (in a nontrivial way) to the setting with cascade click model while retaining their strong performance. Finally, we also briefly discuss the joint ranking and pricing problem and provide an iterative heuristic to calculate an approximate ranking. Managerial implications: Taking into account customers’ click-and-search behavior leads to different structures of the optimal pricing policy, and some common insights under the standard pricing models may no longer hold. Moreover, our simulation studies show that pricing under a (misspecified) classic choice model that is oblivious to customers click-and-search behavior can severely impact profitability. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0504 .