Pricing and Positioning of Horizontally Differentiated Products with Incomplete Demand Information

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 $O(T^{1/2+o(1)})$. 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 $T^{1/2}$, 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.