LP-based Approximation for Personalized Reserve Prices

We study the problem of computing personalized reserve prices in eager second price auctions without having any assumption on valuation distributions. Here, the input is a dataset that contains the submitted bids of n buyers in a set of auctions and the goal is to return personalized reserve prices r that maximize the revenue earned on these auctions by running eager second price auctions with reserve r. We present a novel LP formulation to this problem and a rounding procedure which achieves a (1+2(√2-1)e√2-2)-1≅0.684-approximation. This improves over the 1/2-approximation Algorithm due to Roughgarden and Wang. We show that our analysis is tight for this rounding procedure. We also bound the integrality gap of the LP, which bounds the performance of any algorithm based on this LP.