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Open Access

Power of Second Opportunity: Dynamic Pricing with Second Chance

School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
Naveen Jindal School of Management, University of Texas at Dallas, Richardson, TX 75080, USA
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Abstract

In this paper, we consider the following dynamic pricing problem. Suppose the market price vt of an item arriving at time t is determined by vt=θTxt, where xt is the feature vector of that item and θ is an unknown vector parameter. The seller has to post prices without knowing θ such that the total regret in time span T is minimized. Considering real-world scenarios in which people may negotiate prices, we propose a model called Second Chance Pricing, in which a seller has a second opportunity to post a price after the first offer is declined. Theoretical analysis shows that a second chance of pricing results in a total regret between O(ln⁡Tnln⁡n+1n) and O(n2ln⁡T), where n is the dimension of the feature space. Experiments on both synthetic data and real data demonstrate significant benefits brought about by the second chance where the regret is only 13% of that of one chance.

Keywords

dynamic pricingmultiple pricingregretonline learningellipsoid method

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Tsinghua Science and Technology
Volume 30 Issue 2,
April 2025
Pages 543-560
DOI: 10.26599/TST.2023.9010108
Cite this article:
Ma C, Tang S, Zhang Z. Power of Second Opportunity: Dynamic Pricing with Second Chance. Tsinghua Science and Technology, 2025, 30(2): 543-560. https://doi.org/10.26599/TST.2023.9010108

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Received: 26 July 2023
Revised: 05 September 2023
Accepted: 16 September 2023
Published: 09 December 2024
© The Author(s) 2025.

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
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