Scale-robust Auctions

TL;DR

This paper introduces a scale-robust auction mechanism that maintains near-optimal revenue performance across a wide range of item values by combining second-price and scaled second-price strategies.

Contribution

It proves the optimality of a scale-invariant auction mechanism that randomizes between second-price and a scaled version, ensuring robustness at any scale.

Findings

The mechanism achieves the best multiplicative approximation of optimal revenue.

It is scale invariant and effective for both expensive and cheap items.

The optimal auction randomizes between second-price and 2.45 times second-price.

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.