Mechanism Design for Value Maximizers

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. Likewise, when bidders have no direct utility for leftover money – e.g., because the money comes from a corporate budget – they will naturally buy as much as possible. We call such bidders value maximizers. 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; this contrasts with the case of quasilinear preferences, where Roberts [1979] showed that only affine maximizers are implementable. For general valuations we show that maximizing the value of the highest-value bidder (and iterating through successively lower-value bidders to break ties) 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. We advocate for this generalization, discussing how it and related hybrid auctions can be used to properly handle the complex ad options available in sponsored search today. 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 evaluate the implications of this, establishing 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.