An Improved Welfare Guarantee for First-Price Auctions
We highlight recent progress in worst-case analysis of welfare in first price auctions. It was shown in [Syrgkanis and Tardos 2013] that in any Bayes-Nash equilibrium of a first-price auction, the expected social welfare is at least a (1 - 1/e) approximate to .63-fraction of optimal. This result uses smoothness, the standard technique for worst-case welfare analysis of games, and is tight if bidders' value distributions are permitted to be correlated. With independent distributions, however, the worst-known example, due to [Hartline et al. 2014], exhibits welfare that is a approximate to .89-fraction of optimal. This gap has persisted in spite of the canonical nature of the first-price auction and the prevalence of the independence assumption. In [Hoy et al. 2018], we improve the worst-case lower bound on first-price auction welfare assuming independently distributed values from (1 - 1/e) to approximate to .743. Notably, the proof of this result eschews smoothness in favor of techniques which exploit independence. This note overviews the new approach, and discusses research directions opened up by the result.
Hoy, Darrell, Sam Taggart, and Zihe Wang. 2019. "An Improved Welfare Guarantee for First-Price Auctions." SIGecom Exchanges 17(1): 71-77.
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