# Revenue Maximization and Learning in Products Ranking

arXiv: https://arxiv.org/abs/2012.03800 · HTML: https://mlsanity.com/paper/2012.03800/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Product Ranking for Revenue Maximization with Multiple Purchases](https://mlsanity.com/paper/2210.08268/) (2022)
- [Sequential Choice Bandits with Feedback for Personalizing users' experience](https://mlsanity.com/paper/2101.01572/) (2021)
- [Online Learning of Independent Cascade Models with Node-level Feedback](https://mlsanity.com/paper/2109.02519/) (2021)
- [Learning to Sell a Focal-ancillary Combination](https://mlsanity.com/paper/2207.11545/) (2022)

## Abstract (arXiv)

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, i.e., 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: the consumers have random attention spans instead of fixed ones, 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. sgUsing this fact, we develop an approximation algorithm when only the distribution of the attention spans is given. Under mild conditions, it achieves 1/e 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 tildeO(√T) 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.