Abstract
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) ≈ .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 ≈ .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 ≈ .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.
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