Truthful Outcomes from Non-Truthful Position Auctions

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 can help explain the surprising rarity with which it is used even in settings with unit demand: a relative lack of robustness to inaccuracies in the choice of its parameters. 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.

Sponsored Search Auctions with Rich Ads

“…The first results we present regard how well our heuristic ad allocation algorithm approximates the optimal solution. 6 We report results on a random selection of 100,000 auction instances drawn from Yahoo's Gemini search platform for Desktop devices. An "instance" consists of a set of candidate ads and all relevant accompanying information (bids, clickability predictions, size, decorations, etc.).…”

“…As discussed, to precisely compute prices (say, according to Eq. (6) or Eq. (7)) one needs to compute the allocation curve for the bidder, from which the price can be quickly deduced.…”

“…More broadly, a long line of work starting with Varian [14] and Edelman, Ostrovsky and Schwarz [8] studies GSP and attempts to rationalize its use, e.g., by showing the existence of good equilibria or showing that GSP is more robust when click-through-rates have error [6,13]. More recently, we argue that advertisers do not have quasilinear utilities and that GSP may in fact be the truthful auction [3,16].…”

Mechanism Design for Value Maximizers

“…Initial analyses showed that revenue and welfare in reasonable equilibria are no worse than VCG [Varian, 2007, Edelman et al, 2007. Later studies offered more nuanced analyses -a more recent justification falls out of GSP's simplicity: GSP's equilibrium guarantees are immune to certain errors in click modeling [Milgrom, 2010, Dütting et al, 2016. Unfortunately, none of these results would guide us to invent GSP if it weren't already implemented in practice.…”

GSP - The Cinderella of Mechanism Design

“…Our collective first response was simply "it can't be too bad:" revenue and welfare in reasonable equilibria are no worse than VCG [27,17]. Many studies of GSP followed -a more recent justification falls out of GSP's simplicity: GSP pricing is independent of the likelihood that the user clicks on an ad, 2 so GSP's equilibrium guarantees are immune to errors in click modeling [22,15]. Yet, throughout these and many other results, the community's implicit perspective has remained constant: GSP is an ugly duckling that requires continual excuses.…”