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Pricing and Positioning of Horizontally Differentiated Products with Incomplete Demand Information

Author

Listed:
  • Arnoud V. den Boer

    (Korteweg-de Vries Institute for Mathematics, University of Amsterdam, 1090 GE Amsterdam, Netherlands)

  • Boxiao Chen

    (College of Business Administration, University of Illinois Chicago, Chicago, Illinois 60607)

  • Yining Wang

    (Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080)

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 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.

Suggested Citation

  • Arnoud V. den Boer & Boxiao Chen & Yining Wang, 2024. "Pricing and Positioning of Horizontally Differentiated Products with Incomplete Demand Information," Operations Research, INFORMS, vol. 72(6), pages 2446-2466, November.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:6:p:2446-2466
    DOI: 10.1287/opre.2021.0093
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