# Learning to Sell a Focal-ancillary Combination

arXiv: https://arxiv.org/abs/2207.11545 · HTML: https://mlsanity.com/paper/2207.11545/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 56 references that are in the map.
- First posted on arXiv 23 Jul 2022.

## Builds on (most cited first, 12 of 12)

- [Learning to Optimize via Information-Directed Sampling](https://mlsanity.com/paper/1403.5556/) (2014)
- [Cascading Bandits: Learning to Rank in the Cascade Model](https://mlsanity.com/paper/1502.02763/) (2015)
- [Meta-Thompson Sampling](https://mlsanity.com/paper/2102.06129/) (2021)
- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Meta Dynamic Pricing: Transfer Learning Across Experiments](https://mlsanity.com/paper/1902.10918/) (2019)
- [Combinatorial Cascading Bandits](https://mlsanity.com/paper/1507.04208/) (2015)
- [Dynamic Pricing with Demand Covariates](https://mlsanity.com/paper/1604.07463/) (2016)
- [Distribution-free Contextual Dynamic Pricing](https://mlsanity.com/paper/2109.07340/) (2021)
- [Perishability of Data: Dynamic Pricing under Varying-Coefficient Models](https://mlsanity.com/paper/1701.03537/) (2017)
- [Revenue Maximization and Learning in Products Ranking](https://mlsanity.com/paper/2012.03800/) (2020)
- [Reaping the Benefits of Bundling under High Production Costs](https://mlsanity.com/paper/1512.02300/) (2015)
- [Online Learning and Optimization for Revenue Management Problems with Add-on Discounts](https://mlsanity.com/paper/2005.00947/) (2020)

## Abstract (arXiv)

A number of products are sold in the following sequence: First a focal product is shown, and if the customer purchases, one or more ancillary products are displayed for purchase. A prominent example is the sale of an airline ticket, where first the flight is shown, and when chosen, a number of ancillaries such as cabin or hold bag options, seat selection, insurance etc. are presented. The firm has to decide on a sale format -- whether to sell them in sequence unbundled, or together as a bundle -- and how to price the focal and ancillary products, separately or as a bundle. Since the ancillary is considered by the customer only after the purchase of the focal product, the sale strategy chosen by the firm creates an information and learning dependency between the products: for instance, offering only a bundle would preclude learning customers' valuation for the focal and ancillary products individually. In this paper we study learning strategies for such focal and ancillary item combinations under the following scenarios: (a) pure unbundling to all customers, (b) personalized mechanism, where, depending on some observed features of the customers, the two products are presented and priced as a bundle or in sequence, (c) initially unbundling (for all customers), and switch to bundling (if more profitable) permanently once during the horizon. We design pricing and decisions algorithms for all three scenarios, with regret upper bounded by O(d √T log T), and an optimal switching time for the third scenario.