Optimal Sample Size for Adword Auctions

Generalized Second Price (GSP) mechanism is widely used in ad auctions and reserve price is an effective tool for revenue maximization. The optimal reserve price depends on bidders’ value distribution, which, however, is generally unknown to auctioneers. A common practice for auctioneers is to first collect information about the value distribution by a sampling procedure and then apply the reserve price estimated with the sampled bids to the following auctions. In order to maximize his/her total revenue over finite GSP ad 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 first propose the revenue bounds during and after sampling. Then we formulate the problem of finding the optimal sample size that maximizes the auctioneer’s worse-case total revenue as an constrained optimization problem, the solution of which is independent of the value distribution.