Online Auction Design Using Distribution-Free Uncertainty Quantification with Applications to E-Commerce

TL;DR

COAD introduces a distribution-free approach to online auction design using conditional conformal prediction to quantify bidder-value uncertainty without prespecified value distributions. By incorporating bidder- and item-feature information, COAD constructs bidder-specific lower-bound reserves and a pseudo-virtual value to drive a second-price-like allocation with incentive compatibility and revenue guarantees. The method provides explicit finite-sample coverage guarantees and revenue bounds that improve as more bidders or data are available, and is demonstrated to outperform standard second-price and empirical-Myerson benchmarks on real eBay data and in application-based simulations. The work offers practical, scalable mechanisms for heterogeneous online markets and establishes a bridge between conformal inference and mechanism design with real-world applicability in e-commerce and online advertising.

Abstract

Online auction is a cornerstone of e-commerce, and a key challenge is designing incentive-compatible mechanisms that maximize expected revenue. Existing approaches often assume known bidder value distributions and fixed sets of bidders and items, but these assumptions rarely hold in real-world settings where bidder values are unknown, and the number of future participants is uncertain. In this paper, we introduce the Conformal Online Auction Design (COAD), a novel mechanism that maximizes revenue by quantifying uncertainty in bidder values without relying on known distributions. COAD incorporates both bidder and item features, using historical data to design an incentive-compatible mechanism for online auctions. Unlike traditional methods, COAD leverages distribution-free uncertainty quantification techniques and integrates machine learning methods, such as random forests, kernel methods, and deep neural networks, to predict bidder values while ensuring revenue guarantees. Moreover, COAD introduces bidder-specific reserve prices, based on the lower confidence bounds of bidder valuations, contrasting with the single reserve prices commonly used in the literature. We demonstrate the practical effectiveness of COAD through an application to real-world eBay auction data. Theoretical results and extensive simulation studies further validate the properties of our approach.

Figures (6)

• Figure 1: An illustration of the online auction process.
• Figure 2: Results from Section \ref{['sec:real_data']}, based on 1000 experiments. (a) Average revenue of different mechanisms for auctions of items with various features $z^*$, evaluated using different numbers of data points $N \in \{150, 300, 500, 700\}$. Error bars represent the 95% confidence interval for the mean. (b) Boxplots of the coverage probability of the conformal prediction interval for the true value, conditioned on different item features $z^*$, using different numbers of data points $N \in \{150, 300, 500, 700\}$. The red line denotes the target coverage level of $1 - \alpha = 0.9$.
• Figure 3: Results from Section \ref{['sec:highdsimnn']}, based on 1000 experiments for a randomly selected item. (a) Average revenue of different mechanisms, with varying numbers of $m^*\in \{2,4,6,8,10,12,14\}$ and $N=50000$. (b) Average revenue of different mechanisms, with varying numbers of $m^*\in \{50,100,150,200,250,300\}$ and $N=50000$. (c) Average revenue of different mechanisms, with varying numbers of $N\in\{1000, 3000, 5000, 7000, 9000, 11000, 13000\}$ and $m^*=50$. (d) Boxplots of the coverage probability for the true value, with $N\in\{1000,3000,5000,7000\}$ and $m^*=50$. The red line denotes the target coverage level of $1 - \alpha = 0.9$.
• Figure 4: Results from Section \ref{['poly_high']}, based on 1000 experiments for a randomly selected item. (a) Average revenue of different mechanisms, with varying numbers of $m^*\in \{50,100,150,200,250,300\}$ and $N=20000$. (b) Average revenue of different mechanisms, with varying numbers of $N\in\{1000, 3000, 5000, 7000, 9000, 11000, 13000\}$ and $m^*=50$. (c) Boxplots of the coverage probability for the true value, with varying numbers of $N\in\{1000,3000,5000,7000\}$ and $m^*=50$. The red line denotes the target coverage level $1 - \alpha = 0.9$.
• Figure 5: Results from Section \ref{['low_d']}, based on 1000 experiments. (a) Boxplots of the coverage probability for the true value, conditioned on various $z^*$ with $N=1000$ and $m^*=50$. The red line indicates the target level of $1-\alpha=0.9$. (b) Average revenue of different mechanisms for various features $z^*$, with varying numbers of $m^*\in\{50,100,150,200,250,300,350,400\}$ and $N=5000$. (c) Average revenue of different mechanisms for various features $z^*$, with varying numbers of $N\in\{200, 600, 1000, 1400, 1800\}$ and $m^*=50$.

Theorems & Definitions (9)

• Proposition 1
• Theorem 1
• Theorem 2
• Theorem 3
• Corollary 1
• Corollary 2
• Theorem 4
• Example 1: Comparison with second-price auctions
• Example 2: Comparison with item-specific reserve pricing auctions