Pricing and Positioning of Horizontally Differentiated Products with Incomplete Demand Information
Arnoud V. den Boer, Boxiao Chen, Yining Wang
Operations Research · 2024 · Volume 72 · Issue 6
Abstract
We consider the problem of determining the optimal prices and product configurations of horizontally differentiated products when customers purchase according to a locational (Hotelling) choice model and where the problem parameters are initially unknown to the decision maker. Both for the single-product and multiple-product setting, we propose a data-driven algorithm that learns the optimal prices and product configurations from accumulating sales data, and we show that their regret—the expected cumulative loss caused by not using optimal decisions—after T time periods is 𝑂 ( 𝑇 1 / 2 + 𝑜 ( 1 ) ) O ( T 1 / 2 + o ( 1 ) ) . We accompany this result by showing that, even in the single-product setting, the regret of any algorithm is bounded from below by a constant time 𝑇 1 / 2 T 1 / 2 , implying that our algorithms are asymptotically near optimal. In an extension, we show how our algorithm can be adapted for the case of fixed locations. A numerical study that compares our algorithms with three benchmarks shows that our algorithm is also competitive on a finite time horizon. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2021.0093 .
Keywords
Market Analytics and Revenue Management, horizontal product differentiation, Hotelling model, dynamic pricing, product positioning, incomplete information
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