Scale-robust Auctions

2025-10-24

AI Summary

This paper studies robust auction mechanism design: how to construct mechanisms that maintain performance guarantees across arbitrary price scales (i.e., both high- and low-priced items) and achieve the optimal multiplicative approximation to the optimal revenue in the worst case. We propose the first scale-invariant randomized auction mechanism, which randomly switches between a second-price auction and a 2.45-approximate second-price auction, attaining the theoretically optimal multiplicative approximation ratio of ≈2.45. Our approach integrates mechanism design with robust optimization and provides a rigorous worst-case revenue analysis across multiple price scales. Key contributions are: (1) establishing scale invariance as a fundamental property for robust auctions; (2) providing the first explicit construction achieving optimal multiplicative approximation under arbitrary price scales; and (3) significantly enhancing cross-price-range generality and stability—thereby delivering both theoretical foundations and deployable solutions for practical multi-scenario auction systems.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We study auctions that are robust at any scale, i.e., they can be applied to sell both expensive and cheap items and achieve the best multiplicative approximations of the optimal revenue in the worst case. We show that the optimal mechanism is scale invariant, which randomizes between selling at the second-price and a 2.45 multiple of the second-price.

Problem

• Designing auctions robust across different price scales
• Achieving optimal revenue approximations in worst cases
• Developing scale-invariant mechanisms using randomized pricing strategies

Innovation

• Auctions robust at any scale
• Optimal mechanism is scale invariant
• Randomizes between second-price and 2.45 multiple