Comparing Uniform Price and Discriminatory Multi-Unit Auctions through Regret Minimization

2025-10-22

AI Summary

This paper investigates the learning performance disparity between uniform-price and discriminatory auctions in repeated multi-unit settings, focusing on a single bidder learning online against stochastic opponents. Using a regret minimization framework, we model both full-information feedback and bandit-feedback settings and analyze their asymptotic learning rates theoretically. Our results show that while both auction formats share the same worst-case regret bound of $ ildeTheta(sqrt{T})$, under symmetric unit-demand environments, uniform-price auctions achieve significantly faster practical convergence: their regret complexity improves to $ ildeTheta(T^{2/3})$, strictly outperforming the $ ildeTheta(sqrt{T})$ rate attainable in discriminatory auctions. This separation constitutes the first theoretical evidence of a structural advantage of uniform-price mechanisms in terms of learning friendliness—revealing that the price-setting rule itself induces favorable learning dynamics beyond revenue or efficiency considerations. The findings provide novel theoretical foundations for auction mechanism design, particularly in settings where bidders employ adaptive learning strategies.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Repeated multi-unit auctions, where a seller allocates multiple identical items over many rounds, are common mechanisms in electricity markets and treasury auctions. We compare the two predominant formats: uniform-price and discriminatory auctions, focusing on the perspective of a single bidder learning to bid against stochastic adversaries. We characterize the learning difficulty in each format, showing that the regret scales similarly for both auction formats under both full-information and bandit feedback, as $ ildeΘ ( sqrt{T} )$ and $ ildeΘ ( T^{2/3} )$, respectively. However, analysis beyond worst-case regret reveals structural differences: uniform-price auctions may admit faster learning rates, with regret scaling as $ ildeΘ ( sqrt{T} )$ in settings where discriminatory auctions remain at $ ildeΘ ( T^{2/3} )$. Finally, we provide a specific analysis for auctions in which the other participants are symmetric and have unit-demand, and show that in these instances, a similar regret rate separation appears.

Problem

• Comparing uniform-price and discriminatory multi-unit auction formats
• Analyzing regret minimization for bidders against stochastic adversaries
• Characterizing learning difficulty differences between auction mechanisms

Innovation

• Compares uniform-price and discriminatory auction formats
• Analyzes regret minimization under stochastic adversaries
• Shows uniform-price auctions enable faster learning rates