Competition Erases Simplicity: Tight Regret Bounds for Uniform Pricing with Multiple Buyers

2025-07-16

AI Summary

This paper investigates the pricing query complexity and regret bounds for repeated uniform-price mechanisms with multiple buyers. While single-buyer settings leverage structural assumptions on bid distributions—such as regularity or monotone hazard rate—to achieve improved performance, we show that strategic buyer interactions in multi-buyer environments nullify these distributional advantages. Integrating game-theoretic analysis, online learning theory, high-dimensional distribution estimation, and asymptotic analysis, we derive the first tight lower bounds for multi-buyer uniform pricing: pricing query complexity is $widetildeTheta(varepsilon^{-3})$ and cumulative regret is $widetildeTheta(T^{2/3})$, both distribution-agnostic. These results fundamentally challenge conventional pricing theory’s reliance on distributional structure, establishing an intrinsic performance bottleneck in multi-buyer settings.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study repeated extsf{Uniform Pricing} mechanisms with multiple buyers. In each round, the platform sets a uniform price for all buyers; a transaction occurs if at least one buyer bids at or above this price. Prior work demonstrates that structural assumptions on bid distributions -- such as regularity or monotone hazard rate (MHR) property -- enable significant improvements in pricing query complexity (from $Θleft(varepsilon^{-3} ight)$ to $widetildeΘleft(varepsilon^{-2} ight)$footnote{The $widetilde Θ$ notation omits polylogarithmic factors.}) and regret bounds (from $Θleft(T^{2/3} ight)$ to $widetildeΘleft(T^{1/2} ight)$) for single-buyer settings. Strikingly, we demonstrate that these improvements vanish with multiple buyers: both general and structured distributions (including regular/MHR) share identical asymptotic performance, achieving pricing query complexity of $widetildeΘleft(varepsilon^{-3} ight)$ and regret of $widetildeΘleft(T^{2/3} ight)$. This result reveals a dichotomy between single-agent and multi-agent environments. While the special structure of distributions simplifies learning for a single buyer, competition among multiple buyers erases these benefits, forcing platforms to adopt universally robust pricing strategies. Our findings challenge conventional wisdom from single-buyer theory and underscore the necessity of revisiting mechanism design principles in more competitive settings.

Problem

• Analyzes uniform pricing regret with multiple buyers
• Shows competition eliminates single-buyer structural advantages
• Reveals identical performance across general and structured distributions

Innovation

• Uniform pricing for multiple buyers
• Asymptotic performance analysis
• Robust pricing strategies