Prior-Independent Auctions for Heterogeneous Bidders

TL;DR

This paper develops prior-independent auction mechanisms for selling to heterogeneous bidders with different value distributions, achieving near-optimal revenue approximation or outperforming second-price auctions, with proven optimal trade-offs.

Contribution

It introduces a family of randomized, prior-independent auctions for heterogeneous bidders that balance revenue approximation and second-price performance, extending to multiple items with logarithmic factors.

Findings

Mechanisms approximate optimal revenue or outperform second-price auctions.

The proposed mechanisms are proven optimal for the trade-off between revenue and second-price performance.

Results extend to multi-item settings with logarithmic approximation factors.

Abstract

We study the design of prior-independent auctions in a setting with heterogeneous bidders. In particular, we consider the setting of selling to $n$ bidders whose values are drawn from $n$ independent but not necessarily identical distributions. We work in the robust auction design regime, where we assume the seller has no knowledge of the bidders' value distributions and must design a mechanism that is prior-independent. While there have been many strong results on prior-independent auction design in the i.i.d. setting, not much is known for the heterogeneous setting, even though the latter is of significant practical importance. Unfortunately, no prior-independent mechanism can hope to always guarantee any approximation to Myerson's revenue in the heterogeneous setting; similarly, no prior-independent mechanism can consistently do better than the second-price auction. In light of this, we design a family of (parametrized) randomized auctions which approximates at least one of these benchmarks: For heterogeneous bidders with regular value distributions, our mechanisms either achieve a good approximation of the expected revenue of an optimal mechanism (which knows the bidders' distributions) or exceeds that of the second-price auction by a certain multiplicative factor. The factor in the latter case naturally trades off with the approximation ratio of the former case. We show that our mechanism is optimal for such a trade-off between the two cases by establishing a matching lower bound. Our result extends to selling $k$ identical items to heterogeneous bidders with an additional $O\big(\ln^2 k\big)$-factor in our trade-off between the two cases.