@article{Ma2025, 
author = {Chensheng Ma and Shaojie Tang and Zhao Zhang},
title = {Power of Second Opportunity: Dynamic Pricing with Second Chance},
year = {2025},
journal = {Tsinghua Science and Technology},
volume = {30},
number = {2},
pages = {543-560},
keywords = {online learning, regret, dynamic pricing, multiple pricing, ellipsoid method},
url = {https://www.sciopen.com/article/10.26599/TST.2023.9010108},
doi = {10.26599/TST.2023.9010108},
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.}
}