Designing revenue optimal auctions for selling an item to n symmetric bidders is a fundamental problem in mechanism design. Myerson [1981] shows that the second price auction with an appropriate reserve price is optimal when bidders' values are drawn i.i.d. from a known regular distribution. A cornerstone in the prior-independent revenue maximization literature is a result by Bulow and Klemperer [1996] showing that the second price auction without a reserve achieves (n − 1)/n of the optimal revenue in the worst case. We construct a randomized mechanism that strictly outperforms the second price auction in this setting. Our mechanism inflates the second highest bid with a probability that varies with n. For two bidders we improve the performance guarantee from 0.5 to 0.512 of the optimal revenue. The improvement is based upon a refined analysis of the result by Bulow and Klemperer [1996] , classifying distributions by whether the optimal monopoly price is high. The key to our analysis is to show that for distributions with high reserves, the loss caused by bid inflation in barring the highest bidder is on average offset by the gain from the additional payments. We also resolve a question in the design of revenue optimal mechanisms that have access to a single sample from an unknown distribution. We show that a randomized mechanism strictly outperforms all deterministic mechanisms in terms of worst case guarantee.
5 Second, if a randomized price is allowed, the seller can get a better revenue guarantee by constructing a careful distribution of the price from the single sample REF .