Revenue Maximization for Finitely Repeated Ad Auctions

Reserve price is an effective tool for revenue maximization in ad auctions. The optimal reserve price depends on bidders' value distributions, which, however, are generally unknown to auctioneers. A common practice for auctioneers is to first collect information about the value distributions by a sampling procedure and then apply the reserve price estimated with the sampled bids to the following auctions. In order to maximize the total revenue over finite auctions, it is important for the auctioneer to find a proper sample size to trade off between the cost of the sampling procedure and the optimality of the estimated reserve price. We investigate the sample size optimization problem for Generalized Second Price auctions, which is the most widely-used mechanism in ad auctions, and make three main contributions along this line. First, we bound the revenue losses in the form of competitive ratio during and after sampling. Second, we formulate the problem of finding the optimal sample size as a non-convex mixed integer optimization problem. Then we characterize the properties of the problem and prove the uniqueness of the optimal sample size. Third, we relax the integer optimization problem to a continuous form and develop an efficient algorithm based on the properties to solve it. Experimental results show that our approach can significantly improve the revenue for the auctioneer in finitely repeated ad auctions.