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Feature-Based Dynamic Pricing

Author

Listed:
  • Maxime C. Cohen

    (Desaultels Faculty of Management, McGill University, Montreal, Quebec H3A 1G5, Canada;)

  • Ilan Lobel

    (NYU Stern School of Business, New York, New York 10012;)

  • Renato Paes Leme

    (Google Research, New York, New York 10011)

Abstract

We consider the problem faced by a firm that receives highly differentiated products in an online fashion. The firm needs to price these products to sell them to its customer base. Products are described by vectors of features and the market value of each product is linear in the values of the features. The firm does not initially know the values of the different features, but can learn the values of the features based on whether products were sold at the posted prices in the past. This model is motivated by applications such as online marketplaces, online flash sales, and loan pricing. We first consider a multidimensional version of binary search over polyhedral sets and show that it has a worst-case regret which is exponential in the dimension of the feature space. We then propose a modification of the prior algorithm where uncertainty sets are replaced by their Löwner-John ellipsoids. We show that this algorithm has a worst-case regret which is quadratic in the dimension of the feature space and logarithmic in the time horizon. We also show how to adapt our algorithm to the case where valuations are noisy. Finally, we present computational experiments to illustrate the performance of our algorithm.

Suggested Citation

  • Maxime C. Cohen & Ilan Lobel & Renato Paes Leme, 2020. "Feature-Based Dynamic Pricing," Management Science, INFORMS, vol. 66(11), pages 4921-4943, November.
    • Handle: RePEc:inm:ormnsc:v:66:y:2020:i:11:p:4921-4943
    DOI: 10.1287/mnsc.2019.3485
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    References listed on IDEAS

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    Cited by:

    1. Jianyu Xu & Yu-Xiang Wang, 2023. "Pricing with Contextual Elasticity and Heteroscedastic Valuation," Papers 2312.15999, arXiv.org.
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    3. Jianyu Xu & Yu-Xiang Wang, 2022. "Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise," Papers 2201.11341, arXiv.org, revised Apr 2022.
    4. Jing Xu & Yung-Cheng Hsu & William Biscarri, 2024. "Dynamic Pricing in Securities Lending Market: Application in Revenue Optimization for an Agent Lender Portfolio," Papers 2407.13687, arXiv.org, revised Oct 2024.
    5. Hamsa Bastani & David Simchi-Levi & Ruihao Zhu, 2022. "Meta Dynamic Pricing: Transfer Learning Across Experiments," Management Science, INFORMS, vol. 68(3), pages 1865-1881, March.
    6. Zeqi Ye & Hansheng Jiang, 2023. "Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning," Papers 2310.07558, arXiv.org, revised Oct 2023.
    7. Jianyu Xu & Dan Qiao & Yu-Xiang Wang, 2022. "Doubly Fair Dynamic Pricing," Papers 2209.11837, arXiv.org.
    8. Max Biggs & Rim Hariss & Georgia Perakis, 2023. "Constrained optimization of objective functions determined from random forests," Production and Operations Management, Production and Operations Management Society, vol. 32(2), pages 397-415, February.
    9. Xi Chen & Quanquan Liu & Yining Wang, 2023. "Active Learning for Contextual Search with Binary Feedback," Management Science, INFORMS, vol. 69(4), pages 2165-2181, April.
    10. Nicol`o Cesa-Bianchi & Tommaso Cesari & Roberto Colomboni & Federico Fusco & Stefano Leonardi, 2021. "Bilateral Trade: A Regret Minimization Perspective," Papers 2109.12974, arXiv.org.
    11. Franc{c}ois Bachoc & Tommaso Cesari & Roberto Colomboni, 2024. "A Contextual Online Learning Theory of Brokerage," Papers 2407.01566, arXiv.org.
    12. Nicol`o Cesa-Bianchi & Tommaso Cesari & Roberto Colomboni & Federico Fusco & Stefano Leonardi, 2021. "A Regret Analysis of Bilateral Trade," Papers 2102.08754, arXiv.org.
    13. Qi Feng & J. George Shanthikumar, 2022. "Developing operations management data analytics," Production and Operations Management, Production and Operations Management Society, vol. 31(12), pages 4544-4557, December.
    14. Raad Khraishi & Ramin Okhrati, 2022. "Offline Deep Reinforcement Learning for Dynamic Pricing of Consumer Credit," Papers 2203.03003, arXiv.org.

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