Sebastien Lahaie and Preston McAfee
In the standard model of sponsored search auctions, an ad is ranked according to the product of its bid and its estimated click-through rate (known as the quality score), where the estimates are taken as exact. This paper re-examines the form of the efficient ranking rule when uncertainty in click-through rates is taken into account. We provide a sufficient condition under which applying an exponent---strictly less than one---to the quality score improves expected efficiency. The condition holds for a large class of distributions known as natural exponential families, and for the lognormal distribution. An empirical analysis of Yahoo's sponsored search logs reveals that exponent settings substantially smaller than one can be efficient for both high and low volume keywords, implying substantial deviations from the traditional ranking rule.
In Workshop on Internet and Network Economics (WINE)