Optimal Auctions vs. Anonymous Pricing

TL;DR

This paper demonstrates that anonymous pricing approximates the revenue of optimal auctions within a factor of e, showing that simple pricing strategies are nearly as effective as complex auctions in single-item settings.

Contribution

It proves that the worst-case revenue ratio of anonymous pricing to the optimal auction is e, improving previous bounds from four to e.

Findings

Anonymous pricing approximates optimal revenue within a factor of e.

Discrimination and simultaneity are less critical for revenue in single-item auctions.

The bound on the approximation ratio is tightened from four to e.

Abstract

For selling a single item to agents with independent but non-identically distributed values, the revenue optimal auction is complex. With respect to it, Hartline and Roughgarden (2009) showed that the approximation factor of the second-price auction with an anonymous reserve is between two and four. We consider the more demanding problem of approximating the revenue of the ex ante relaxation of the auction problem by posting an anonymous price (while supplies last) and prove that their worst-case ratio is e. As a corollary, the upper-bound of anonymous pricing or anonymous reserves versus the optimal auction improves from four to $e$. We conclude that, up to an $e$ factor, discrimination and simultaneity are unimportant for driving revenue in single-item auctions.