Revenue guarantees in sponsored search auctions

Sponsored search auctions are the main source of revenue for search engines. In such an auction, a set of utility-maximizing advertisers compete for a set of ad slots. The assignment of advertisers to slots depends on bids they submit; these bids may be different than the true valuations of the advertisers for the slots. Variants of the celebrated VCG auction mechanism guarantee that advertisers act truthfully and, under mild assumptions, lead to revenue or social welfare maximization. Still, the sponsored search industry mostly uses generalized second price (GSP) auctions; these auctions are known to be non-truthful and suboptimal in terms of social welfare and revenue. In an attempt to explain this tradition, we study a Bayesian setting where the valuations of advertisers are drawn independently from a regular probability distribution. In this setting, it is well known by the work of Myerson (1981) that the optimal revenue is obtained by the VCG mechanism with a particular reserve price that depends on the probability distribution. We show that by appropriately setting the reserve price, the revenue over any Bayes-Nash equilibrium of the game induced by the GSP auction is at most a small constant fraction of the optimal revenue, improving recent results of Lucier, Paes Leme, and Tardos (2012). Our analysis is based on the Bayes-Nash equilibrium conditions and on the properties of regular probability distributions .