Nontruthful Position Auctions Are More Robust to Misspecification

We consider the classical model of sponsored search due to Edelman et al. and Varian and examine how robust standard position auctions are to a misspecification of the position-dependent quality factors used by this model. We show that under both complete and incomplete information a nontruthful position auction admits an efficient equilibrium for a strictly broader range of parameter values than the Vickrey-Clarke-Groves (VCG) mechanism, which would be truthful if the parameters were specified correctly. Our result for complete information concerns the generalized second-price (GSP) mechanism and is driven by a detailed understanding of the Nash equilibrium polytopes of the VCG mechanism and the GSP mechanism. Our result for incomplete information concerns the generalized first-price (GFP) mechanism and uses a surprising connection between the unique candidate equilibrium bidding functions of the VCG mechanism and the GFP mechanism.