IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2312.15999.html
   My bibliography  Save this paper

Pricing with Contextual Elasticity and Heteroscedastic Valuation

Author

Listed:
  • Jianyu Xu
  • Yu-Xiang Wang

Abstract

We study an online contextual dynamic pricing problem, where customers decide whether to purchase a product based on its features and price. We introduce a novel approach to modeling a customer's expected demand by incorporating feature-based price elasticity, which can be equivalently represented as a valuation with heteroscedastic noise. To solve the problem, we propose a computationally efficient algorithm called "Pricing with Perturbation (PwP)", which enjoys an $O(\sqrt{dT\log T})$ regret while allowing arbitrary adversarial input context sequences. We also prove a matching lower bound at $\Omega(\sqrt{dT})$ to show the optimality regarding $d$ and $T$ (up to $\log T$ factors). Our results shed light on the relationship between contextual elasticity and heteroscedastic valuation, providing insights for effective and practical pricing strategies.

Suggested Citation

  • Jianyu Xu & Yu-Xiang Wang, 2023. "Pricing with Contextual Elasticity and Heteroscedastic Valuation," Papers 2312.15999, arXiv.org.
  • Handle: RePEc:arx:papers:2312.15999
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2312.15999
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Maxime C. Cohen & Adam N. Elmachtoub & Xiao Lei, 2022. "Price Discrimination with Fairness Constraints," Management Science, INFORMS, vol. 68(12), pages 8536-8552, December.
    2. Gah-Yi Ban & N. Bora Keskin, 2021. "Personalized Dynamic Pricing with Machine Learning: High-Dimensional Features and Heterogeneous Elasticity," Management Science, INFORMS, vol. 67(9), pages 5549-5568, September.
    3. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
    4. Yining Wang & Boxiao Chen & David Simchi-Levi, 2021. "Multimodal Dynamic Pricing," Management Science, INFORMS, vol. 67(10), pages 6136-6152, October.
    5. Maxime C. Cohen & Ilan Lobel & Renato Paes Leme, 2020. "Feature-Based Dynamic Pricing," Management Science, INFORMS, vol. 66(11), pages 4921-4943, November.
    6. Mila Nambiar & David Simchi-Levi & He Wang, 2019. "Dynamic Learning and Pricing with Model Misspecification," Management Science, INFORMS, vol. 65(11), pages 4980-5000, November.
    7. Josef Broder & Paat Rusmevichientong, 2012. "Dynamic Pricing Under a General Parametric Choice Model," Operations Research, INFORMS, vol. 60(4), pages 965-980, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zeqi Ye & Hansheng Jiang, 2023. "Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning," Papers 2310.07558, arXiv.org, revised Oct 2023.
    2. 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.
    3. Boxiao Chen & David Simchi-Levi & Yining Wang & Yuan Zhou, 2022. "Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information," Management Science, INFORMS, vol. 68(8), pages 5684-5703, August.
    4. 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.
    5. Woonghee Tim Huh & Michael Jong Kim & Meichun Lin, 2022. "Bayesian dithering for learning: Asymptotically optimal policies in dynamic pricing," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3576-3593, September.
    6. Yiwei Chen & Cong Shi, 2023. "Network revenue management with online inverse batch gradient descent method," Production and Operations Management, Production and Operations Management Society, vol. 32(7), pages 2123-2137, July.
    7. Gah-Yi Ban & N. Bora Keskin, 2021. "Personalized Dynamic Pricing with Machine Learning: High-Dimensional Features and Heterogeneous Elasticity," Management Science, INFORMS, vol. 67(9), pages 5549-5568, September.
    8. Jinzhi Bu & David Simchi-Levi & Yunzong Xu, 2022. "Online Pricing with Offline Data: Phase Transition and Inverse Square Law," Management Science, INFORMS, vol. 68(12), pages 8568-8588, December.
    9. Jianyu Xu & Dan Qiao & Yu-Xiang Wang, 2022. "Doubly Fair Dynamic Pricing," Papers 2209.11837, arXiv.org.
    10. Jianqing Fan & Yongyi Guo & Mengxin Yu, 2021. "Policy Optimization Using Semi-parametric Models for Dynamic Pricing," Papers 2109.06368, arXiv.org, revised May 2022.
    11. Nicol`o Cesa-Bianchi & Tommaso Cesari & Roberto Colomboni & Federico Fusco & Stefano Leonardi, 2021. "Bilateral Trade: A Regret Minimization Perspective," Papers 2109.12974, arXiv.org.
    12. Sentao Miao & Xi Chen & Xiuli Chao & Jiaxi Liu & Yidong Zhang, 2022. "Context‐based dynamic pricing with online clustering," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3559-3575, September.
    13. Arnoud V. den Boer & N. Bora Keskin, 2022. "Dynamic Pricing with Demand Learning and Reference Effects," Management Science, INFORMS, vol. 68(10), pages 7112-7130, October.
    14. Nicol`o Cesa-Bianchi & Tommaso Cesari & Roberto Colomboni & Federico Fusco & Stefano Leonardi, 2021. "A Regret Analysis of Bilateral Trade," Papers 2102.08754, arXiv.org.
    15. Liu, Jianing & Wen, Xiao & Jian, Sisi, 2024. "Toward better equity: Analyzing travel patterns through a neural network approach in mobility-as-a-service," Transport Policy, Elsevier, vol. 153(C), pages 110-126.
    16. Junichi Minagawa & Thorsten Upmann, 2019. "Price Effects on Compound Commodities," Scandinavian Journal of Economics, Wiley Blackwell, vol. 121(2), pages 630-646, April.
    17. William L. Cooper & Tito Homem-de-Mello & Anton J. Kleywegt, 2015. "Learning and Pricing with Models That Do Not Explicitly Incorporate Competition," Operations Research, INFORMS, vol. 63(1), pages 86-103, February.
    18. Mervyn Allister King, 1993. "Debt Deflation: Theory and Evidence," FMG Discussion Papers dp175, Financial Markets Group.
    19. Xiao, Baichun & Yang, Wei, 2021. "A Bayesian learning model for estimating unknown demand parameter in revenue management," European Journal of Operational Research, Elsevier, vol. 293(1), pages 248-262.
    20. N. Bora Keskin & Assaf Zeevi, 2014. "Dynamic Pricing with an Unknown Demand Model: Asymptotically Optimal Semi-Myopic Policies," Operations Research, INFORMS, vol. 62(5), pages 1142-1167, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2312.15999. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.