Multiproduct Dynamic Pricing with Limited Inventories Under a Cascade Click Model

Problem definition: Designing effective operational strategies requires a good understanding of customer behavior. The classic economic theory of customer choice has long been the underlying paradigm in the operations and management science literature. However, the rise of online marketplaces such as e-commerce websites has triggered considerable efforts both in the academia and industry to develop alternative models that not only provide a good approximation of customer behavior on such platforms but also are easily scalable for large-scale implementations. In this paper, we consider a multi-product 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. This result is reminiscent of the classic upper-bound result in the standard revenue management (RM) setting, whose importance on RM research in the past two decades cannot be overstated. Third, we show that two heuristic policies that are known to have strong performance guarantees in the standard RM setting can be properly adapted (albeit in a non-trivial way) to the setting with Cascade Click model while retaining their strong performance guarantees. 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 of the common insights under the standard pricing models may no longer hold. In fact, our simulation studies show that pricing under a (mis-specified) classic choice model that is oblivious to customers click-and-search behavior can severely impact profitability. In terms of practical implications, our heuristic policies show the ``tractability'' of Cascade Click model for making operational decisions. Finally, our simulation studies show a significant revenue increase of more than 10% can be attained when the display ranking and pricing of the products are jointly optimized, which highlights the importance of synchronizing the two decisions.