Position Auctions with Bidder-Specific Minimum Prices

Position auctions such as the Generalized Second Price (GSP) are commonly used for sponsored search, e.g., by Yahoo! and Google. We now have an understanding of the equilibria of these auctions, via game-theoretic concepts like Generalized English Auctions and the “locally envy-free” property, as well as through a relationship to the well-known, truthful Vickrey-Clarke-Groves (VCG) mechanism. In practice, however, position auctions are implemented with additional constraints, in particular, bidder-specific minimum prices. Such minimum prices are used to control the quality of the ads that appear on the page. We study the effect of bidder-specific minimum prices in position auctions. Näıvely enforcing minimum prices in the VCG mechanism breaks the truthfulness of the auction; we describe two variants of VCG for which revealing the truth is a dominant strategy. The implications of bidder-specific minimum prices are more intricate for the GSP auction. Some properties proved for standard GSP no longer hold in this setting. For example, we show that the GSP allocation is now not always efficient (in terms of advertiser value). Also, the property of“envy-locality”enjoyed by GSP—which is essential in the prior analysis of strategies and equilibria— no longer holds. Our main result is to show that despite losing envy locality, GSP with bidder-specific minimum prices still has an envy-free equilibrium.