Optimal Pricing For MHR Distributions

10/01/2018

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by   Yiannis Giannakopoulos, et al.

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We study the performance of anonymous posted-price selling mechanisms for a standard Bayesian auction setting, where n bidders have i.i.d. valuations for a single item. We show that for the natural class of Monotone Hazard Rate (MHR) distributions, offering the same, take-it-or-leave-it price to all bidders can achieve an (asymptotically) optimal revenue. In particular, the approximation ratio is shown to be 1+O( n / n), matched by a tight lower bound for the case of exponential distributions. This improves upon the previously best-known upper bound of e/(e-1)≈ 1.58 for the slightly more general class of regular distributions. In the worst case (over n), we still show a global upper bound of 1.35. We give a simple, closed-form description of our prices which, interestingly enough, relies only on minimal knowledge of the prior distribution, namely just the expectation of its second-highest order statistic.