Pricing and Positioning of Horizontally Differentiated Products with Incomplete Demand Information
Posted: 10 Sep 2020
Date Written: August 28, 2020
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)}). 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 times T^{1/2}, implying that our algorithms are asymptotically near-optimal. A numerical study that compares our algorithms to a benchmark shows that our algorithm is also competitive on a finite time horizon.
Keywords: Horizontal Product Differentiation, Hotelling Model, Dynamic Pricing, Product Positioning, Incomplete Information
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