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Pricing with Contextual Elasticity and Heteroscedastic Valuation

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  • 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
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    References listed on IDEAS

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    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.
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