Non-Truthful Position Auctions Are More Robust to Misspecification

Abstract: In the standard single-dimensional model of position auctions, bidders agree on the relative values of the positions and each of them submits a single bid that is interpreted in terms of these values. Motivated by current practice in sponsored search we consider a situation where the auctioneer uses estimates of the relative values, which may be imprecise, and show that under both complete and incomplete information a non-truthful mechanism is able to support an efficient outcome in equilibrium for a wider range of these estimates than the VCG mechanism. We thus exhibit a property of the VCG mechanism that may help explain the surprising rarity with which it is used even in settings with unit demand, a relative lack of robustness to misspecification of the bidding language. The result for complete information concerns the generalized second-price mechanism and lends additional theoretical support to the use of this mechanism in practice. Particularly interesting from a technical perspective is the result for incomplete information, which is driven by a surprising connection between equilibrium bids in the VCG mechanism and the generalized first-price mechanism.