Optimal Pricing for MHR and λ-regular Distributions

We study the performance of anonymous posted-price selling mechanisms for a standard Bayesian auction setting, where n bidders have i.i.d. valuations single item. show that natural class Monotone Hazard Rate (MHR) distributions, offering same, take-it-or-leave-it price to all can achieve an (asymptotically) optimal revenue. In particular, approximation ratio is shown be 1+ O (ln ln / ), matched by tight lower bound case exponential distributions. This improves upon previously best-known upper e /( −1)≈ 1.58 slightly more general regular worst (over we still global 1.35. give simple, closed-form description our prices, which, interestingly enough, relies only on minimal knowledge prior distribution, namely, just expectation its second-highest order statistic. Furthermore, extend techniques handle λ-regular distributions interpolate between MHR (λ =0) and =1). Our pricing rule now results in asymptotic ranges smoothly, with respect λ, from 1 (MHR distributions) −1) (regular distributions). Finally, explicitly continuous provide matching bounds, every λ.