stat.MLOct 15, 2026

Source-Aware Dynamic Pricing with Strategic Buyers

Authors: Jinjiang Zou, Yang Li, Zemin Zheng

Organizations: School of Management, University of Science and Technology of China, Hefei 230026, China

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Abstract

In modern commerce, firms and platforms typically use customer features from different sources to personalize prices: some features are verified using seller records or third-party data, while others are self-reported and may be strategically manipulated by buyers seeking lower prices. We therefore introduce a novel source-aware framework for contextual dynamic pricing with strategic buyers in a high-dimensional semiparametric setting, where buyer valuations follow a sparse linear model with an unknown noise distribution. To account for differences in manipulability across feature sources while enabling effective valuation learning, we develop the Source-Aware Localized exploration and calibrated Exploitation (SALE) pricing policy, which draws on verified features to localize price exploration and combines verified and reported features to correct for strategic manipulation during exploitation. Our localized exploration design allows converting binary purchase feedback into unbiased signals of conditional mean valuations, yielding a new population equation that supports consistent sparse estimation despite non-i.i.d. buyer arrivals. Building on this estimate, we develop a localized empirical-process analysis that exploits intrinsic sparse geometry to establish uniform guarantees for nonparametric estimation of the noise distribution in the high-dimensional setting. With these estimation guarantees, we establish SALE's self-recovery property, which keeps localized exploration valid with high probability and leads to a sublinear expected regret bound. Both simulation studies and real-data experiments demonstrate the appealing performance of SALE. To the best of our knowledge, our study is the first to provide a theoretical and practical framework for incorporating information provenance into dynamic pricing with strategic buyers.

Figures & tables

Figure 1: Information structure in source-aware personalized pricing. Buyer valuation depends on true features, whereas the seller bases pricing decisions on verified features and potentially manipulated reports.
Figure 2: Pricing rules in exploration and exploitation.
Figure 3: Personalized exploration and calibrated Exploitation across episodes.
Figure 4: Cumulative expected regret across feature-source compositions ( d=50,s0=6,B=100,T=204,600d=50,s_{0}=6,B=100,T=204{,}600 ; 50 replications). Total slope energy, verified signal share, and manipulation strength are held fixed.
Figure 5: Localized-acquisition mechanism under a fixed valuation law ( d=50,s0=6,T=204,600d=50,s_{0}=6,T=204{,}600 ; 50 replications). Only the admissible price cap BB varies across the horizontal axis.
Figure 6: Cumulative expected regret with known manipulation cost ( s0=6,B=140,T=819,000s_{0}=6,B=140,T=819{,}000 ; 20 replications). The panels vary d∈{300,600,1000}d\in\{300,600,1000\} . Shaded regions show one Monte Carlo standard error.
Figure 7: Unknown manipulation cost ( d=50,s0=6,B=100,T=204,600d=50,s_{0}=6,B=100,T=204{,}600 ; 50 replications). The first two panels report cumulative expected regret. The third reports usable matched records and SALE-U’s relative response-estimation error. The displayed repeat-buyer percentages refer to the repeat-buyer rate τ\tau .
Figure 8: Pricing-map comparison under smooth asymmetric market noise ( d=2,s0=3,m=3,B=15,T=819,000d=2,s_{0}=3,m=3,B=15,T=819{,}000 ; 50 replications). The comparator replaces only SALE-K’s semiparametric pricing map by a standard-Gaussian working model.
Figure 9: AutoLoan semi-synthetic experiment ( d=66,d_{\mathrm{V}}=64,s_{0}=8,B=\60{,}000,T=819{,}000$ ; 30 replications). The left panel compares all three policies, and the right panel enlarges the SALE–Blind ETC comparison. Shaded regions show one Monte Carlo standard error.
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