Tight Approximation Ratio of Anonymous Pricing

We consider two canonical Bayesian mechanism design settings. In the single-item setting, we prove tight approximation ratio for anonymous pricing: compared with Myerson Auction, it extracts at least frac12.62-fraction of revenue; there is a matching lower-bound example. In the unit-demand single-buyer setting, we prove tight approximation ratio between the simplest and optimal deterministic mechanisms: in terms of revenue, uniform pricing admits a 2.62-approximation of item pricing; we further validate the tightness of this ratio. These results settle two open problems asked in~citeH13,CD15,AHNPY15,L17,JLTX18. As an implication, in the single-item setting: we improve the approximation ratio of the second-price auction with anonymous reserve to 2.62, which breaks the state-of-the-art upper bound of e ≈ 2.72.