Revenue Maximization and Learning in Product Ranking
Abstract
We consider the revenue maximization problem for an online retailer who plans to display in order a set of products differing in their prices and qualities. Consumers have attention spans, that is, the maximum number of products they are willing to view, and inspect the products sequentially before purchasing a product or leaving the platform empty-handed when the attention span gets exhausted. Our framework extends the well-known cascade model in two directions: random attention spans of a representative customer are captured and the firm maximizes revenues instead of clicking probabilities. We show a nested structure of the optimal product ranking as a function of the attention span when the attention span is fixed. Using this fact, we develop an approximation algorithm when only the distribution of the attention spans is given. Under mild conditions, it achieves of the revenue of the clairvoyant case when the realized attention span is known. We also show that no algorithms can achieve more than 0.5 of the revenue of the same benchmark. The model and the algorithm can be generalized to the ranking problem when consumers make multiple purchases. When the conditional purchase probabilities are not known and may depend on consumer and product features, we devise an online learning algorithm that achieves regret relative to the approximation algorithm, despite the censoring of information: the attention span of a customer who purchases an item is not observable. Numerical experiments demonstrate the outstanding performance of the approximation and online learning algorithms.
Funding: The research of N. Chen was supported by the NSERC Discovery Grant. The research of A. Li was supported by the Hong Kong Research Grants Council’s General Research Fund [Grant 14509124].
Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2020.0781.
