The generalized second price (GSP) auction has served as the core selling mechanism for sponsored search ads for over a decade. However, recent trends expanding the set of allowed ad formats---to include a variety of sizes, decorations, and other distinguishing features---have raised critical problems for GSP-based platforms. Alternatives such as the Vickrey-Clarke-Groves (VCG) auction raise different complications because they fundamentally change the way prices are computed. In this paper we report on our efforts to redesign a search ad selling system from the ground up in this new context, proposing a mechanism that optimizes an entire slate of ads globally and computes prices that achieve properties analogous to those held by GSP in the original, simpler setting of uniform ads. A careful algorithmic coupling of allocation-optimization and pricing-computation allows our auction to operate within the strict timing constraints inherent in real-time ad auctions. We report performance results of the auction in Yahoo's Gemini Search platform.
More broadly, a long line of work starting with Varian @cite_8 and Edelman, Ostrovsky and Schwarz @cite_5 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 @cite_2 @cite_13 . More recently, we argue that advertisers do not have quasilinear utilities and that GSP may in fact be the truthful auction @cite_0 @cite_3 .
@cite_8 @cite_3 @cite_0 @cite_2 @cite_5 @cite_13
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Bidders often want to get as much as they can without violating constraints on what they spend. For example, advertisers seek to maximize the impressions, clicks, sales, or market share generated by their advertising, subject to budget or return-on-investment (ROI) constraints. The quasilinear utility model dramatically fails to capture these preferences, and so we initiate the study of mechanism design in this different context. In single-parameter settings, we show that any monotone allocation can be implemented truthfully. Interestingly, even in unrestricted domains any choice function that optimizes monotone functions of bidders' values can be implemented. For general valuations we show that maximizing the value of the highest-value bidder is the natural analog of welfare maximization. We apply our results to online advertising as a case study. Firstly, the natural analog of welfare maximization directly generalizes the generalized second price (GSP) auction commonly used to sell search ads. Finally, we show that value-maximizing preferences are robust in a practical sense: even though real advertisers' preferences are complex and varied, as long as outcomes are "sufficiently different," any advertiser with a moderate ROI constraint and "super-quasilinear" preferences will be behaviorally equivalent to a value maximizer. We empirically establish that for at least 80 of a sample of auctions from the Yahoo Gemini Native ads platform, bidders requiring at least a 100 ROI should behave like value maximizers. We 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. For a standard position auction environment in which the auctioneer may not know the precise relative values of the positions, we show that under both complete and incomplete information a non-truthful mechanism supports the truthful outcome of the VCG mechanism for a wider range of these values than the VCG mechanism itself. 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 case of incomplete information, where a surprising combinatorial equivalence helps us to avoid confrontation with an unwieldy differential equation. A mechanism can be simplified by restricting its message space. If the restricted message spaces satisfy a certain "outcome closure property," then the simplification is "tight": for every [epsilon][greater-or-equal, slanted]0, any [epsilon]-Nash equilibrium of the simplified mechanism is also an [epsilon]-Nash equilibrium of the unrestricted mechanism. Prominent auction and matching mechanisms are tight simplifications of mechanisms studied in economic theory and often incorporate price-adjustment features that facilitate simplification. The generalized second-price auction used for sponsored-search advertising is a tight simplification of a series of second-price auctions that eliminates the lowest revenue equilibrium outcomes and leaves intact only higher revenue equilibria. We investigate the "generalized second price" auction (GSP), a new mechanism which is used by search engines to sell online advertising that most Internet users encounter daily. GSP is tailored to its unique environment, and neither the mechanism nor the environment have previously been studied in the mechanism design literature. Although GSP looks similar to the Vickrey-Clarke-Groves (VCG) mechanism, its properties are very different. In particular, unlike the VCG mechanism, GSP generally does not have an equilibrium in dominant strategies, and truth-telling is not an equilibrium of GSP. To analyze the properties of GSP in a dynamic environment, we describe the generalized English auction that corresponds to the GSP and show that it has a unique equilibrium. This is an ex post equilibrium that results in the same payoffs to all players as the dominant strategy equilibrium of VCG.