Tight Approximation Ratio of Anonymous Pricing.

This paper considers two canonical Bayesian mechanism design settings. In the single-item setting, the tight approximation ratio of Anonymous Pricing is obtained: (1) compared to Myerson Auction, Anonymous Pricing always generates at least a 1/2.62-fraction of the revenue; (2) there is a matching lower-bound instance. In the unit-demand single-buyer setting, the tight approximation ratio between the simplest deterministic mechanism and the optimal deterministic mechanism is attained: in terms of revenue, (1) Uniform Pricing admits a 2.62-approximation to Item Pricing; (2) a matching lower-bound instance is presented also. These results answer two open questions asked by Alaei et al. (FOCS’15) and Cai and Daskalakis (GEB’15). As an implication, in the single-item setting: the approximation ratio of Second-Price Auction with Anonymous Reserve (Hartline and Roughgarden EC’09) is improved to 2.62, which breaks the best known upper bound of e ≈ 2.72.