Adverse Selection and Auction Design for Internet Display Advertising

Abstract

Note that for any allocation rule z, the quantities V B (z), V P (z) and V (z) depend implicitly on the number of bidders and the distributions of advertiser values. At times, we study the variation in the performance of an allocation rule z, as a function of an underlying parameter θ (such as the number of bidders or the distribution from which their values are drawn). In some cases, we make the dependence on θ explicit by writing V (z; θ). Throughout the appendix, we use the letter µ to refer to the brand advertiser's expected match value E[M 0 ]. PROOF OF PROPOSITION 1:We must show that second price auctions cannot guarantee ( 1 2 + )V (OMN), for any > 0. Fix N ≥ 2 and > 0. To do so, we assume that M i are iid draws from a power law distribution with parameter a, and maintain the identity]. As a ↓ 1, it becomes possible to capture nearly all of the value from performance advertisers by allocating to them a vanishingly small fraction of impressions. Thus,Choose a sufficiently close to one such that V (OMN) > 2E[M (1) ]E[C]. Let C be drawn from a power law distribution with parameter a . By Lemma 1, if a is sufficiently close to one, then sup b V (SP b ) = γµE[C] = (1 + )E[M (1) ]E[C]. It follows that sup b V (SP b )/V (OMN) < 1+ 2 . LEMMA 1: Suppose that M (1) ∼ F , which has density f on [0, ∞), and that E[M 1+ (1) ] < ∞ for some > 0. Fix γµ = γE[M 0 ] > E[M (1) ]. Suppose that C ∈ [1, ∞) has density g(c) = a c −a −1 . Then there exists δ > 0 such that if a < 1 + δ, sup b V (SP b ) = γµE[C].

Discovering Auctions: Contributions of Paul Milgrom and Robert Wilson*

“…This work paved the way for new applications of auctions and other price discovery mechanisms in a range of market design contexts: everything from selling online advertising (Edelman et al ., 2007; Lahaie et al ., 2007; Varian, 2007, 2009; Agarwal et al ., 2009; Athey and Ellison, 2011; Varian and Harris, 2014; Arnosti et al ., 2016; Ostrovsky and Schwarz, 2016) and trading financial securities (Budish et al ., 2015; Du and Zhu, 2017; Duffie and Zhu, 2017; Kyle and Lee, 2017) to allocating food to food banks (Prendergast, 2017, 2020). More broadly, the work of Milgrom and Wilson has fed into a growing understanding – also pushed by Roth (2002) and others – of the role of the economist as an “engineer”, working to improve real‐world markets through constant feedback between theory and practice.…”

Boosted Second Price Auctions

“…The design of the BSP auction bears some resemblance to the mechanism in [3]. The aforementioned paper studies adverse selection in online ad markets for the impressions that are sold via auctions versus guaranteed-delivery contracts, where the valuations of the buyers are correlated via a common value component.…”