Expressive auctions for externalities in online advertising.

When online ads are shown together, they compete for user attention and conversions, imposing negative externalities on each other. While the competition for user attention in sponsored search can be captured via models of clickthrough rates, the post-click competition for conversions cannot: since the value-per-click of an advertiser is proportional to the conversion probability conditional on a click, which depends on the other ads displayed, the private value of an advertiser is no longer one-dimensional, and the GSP mechanism is not adequately expressive. We study the design of expressive GSP-like mechanisms for the simplest form that an advertiser's private value can have in the presence of such externalities- an advertiser's value depends on exclusivity, i.e., whether her ad is shown exclusively, or along with other ads. Our auctions take as input two-dimensional (per-click) bids for exclusive and nonexclusive display, and have two types of outcomes: either a single ad is displayed exclusively, or multiple ads are simultaneously shown. We design two expressive auctions that are both extensions of GSP- the first auction, GSP2D, is designed with the property that the allocation and pricing are identical to GSP when multiple ads are shown; the second auction, NP2D, is designed to be a next price auction. We show that both auctions have high efficiency and revenue in all reasonable equilibria; further, the NP2D auction is guaranteed to always have an equilibrium with revenue at least as much as the current GSP mechanism. However, we find that unlike with one-dimensional valuations, the GSP-like auctions for these richer valuations do not always preserve efficiency and revenue with respect to the VCG mechanism.