Pricing with Contextual Elasticity and Heteroscedastic Valuation

• URL: http://arxiv.org/abs/2312.15999v1
• Date: Tue, 26 Dec 2023 11:07:37 GMT
• Title: Pricing with Contextual Elasticity and Heteroscedastic Valuation
• Authors: Jianyu Xu, Yu-Xiang Wang
• Abstract summary: 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. Our results shed light on the relationship between contextual elasticity and heteroscedastic valuation, providing insights for effective and practical pricing strategies.
• Score: 23.96777734246062
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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