Pricing and Positioning of Horizontally Differentiated Products with Incomplete Demand Information

63 Pages Posted: 10 Sep 2020 Last revised: 29 Jan 2021

See all articles by Arnoud V. den Boer

Arnoud V. den Boer

University of Amsterdam - Korteweg-de Vries Institute for Mathematics; University of Amsterdam Business School

Boxiao Chen

University of Illinois at Chicago - College of Business Administration

Yining Wang

University of Florida - Warrington College of Business Administration

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

Suggested Citation

den Boer, Arnoud V. and Chen, Boxiao and Wang, Yining, Pricing and Positioning of Horizontally Differentiated Products with Incomplete Demand Information (August 28, 2020). Available at SSRN: https://ssrn.com/abstract=3682921 or http://dx.doi.org/10.2139/ssrn.3682921

Arnoud V. Den Boer

University of Amsterdam - Korteweg-de Vries Institute for Mathematics ( email )

Netherlands

University of Amsterdam Business School ( email )

Roetersstraat 18
Amsterdam, 1018WB
Netherlands

Boxiao Chen (Contact Author)

University of Illinois at Chicago - College of Business Administration ( email )

601 S Morgan St
Chicago, IL 60607
United States

Yining Wang

University of Florida - Warrington College of Business Administration ( email )

Gainesville, FL 32611
United States

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