An improved welfare guarantee for first-price auctions

Abstract

This paper proves that the welfare of the first price auction in Bayes-Nash equilibrium is at least a .743-fraction of the welfare of the optimal mechanism assuming agents' values are independently distributed. The previous best bound was 1 − 1/e ≈ .63, derived in Syrgkanis and Tardos (2013) using smoothness, the standard technique for reasoning about welfare of games in equilibrium. In the worst known example (from Hartline et al. (2014)), the first price auction achieves a ≈ .869-fraction of the optimal welfare, far better than the theoretical guarantee. Despite this large gap, it was unclear whether the 1 − 1/e ≈ .63 bound was tight. We prove that it is not. Our analysis eschews smoothness, and instead uses the independence assumption on agents' value distributions to give a more careful accounting of the welfare contribution of agents who win despite not having the highest value.

Simple, Credible, and Approximately-Optimal Auctions

“…Hartline, Hoy, and Taggart [HHT14] develop a framework for bounding the fraction of optimal revenue obtained at equilibrium in various single-item auction formats, such as first-price and all-pay auctions. Our analysis of the typeloss trade-off for different auction formats shares inspiration from their equilibrium analysis, as well as from the literature bounding the welfare of equilibria in first-price auctions [ST13,HTW19].…”