Cost of Conciseness in Sponsored Search Auctions

URL:

http://www2007.org/workshops/paper_79.pdf

Abstract:

We study keyword auctions in a setting where bidders have a vector of values for slots, and a bidder's value for a slot is not necessarily proportional to the expected number of clicks in that slot. Specifically, bidders need not only derive values from clicks on their ad, nor do they need to value clicks in all slots equally. This is the most general model of bidder valuations (without externalities) in sponsored search, and encompasses a variety of advertising objectives, including conversions and branding. We study the properties of the generalized second price auction when bidders with such vector values report a single scalar bid to the auction (we assume that bidders and the auctioneer agree on a ranking of the slots). We compare against the efficient, welfare maximizing outcome of the VCG mechanism with input as the full vector of values. Surprisingly, we find that there always exists an equilibrium corresponding to the VCG outcome, when bids and prices are per-impression in the generalized second price auction. If bids and prices are per-click, this need not be the case: in fact, an equilibrium need not even exist. However, under monotonicity conditions on the valuations of bidders and clickthrough rates, the VCG outcome is indeed an equilibrium of the system. Finally, we discuss the problem of bidding strategies leading to such efficient equilibria: contrary to the case when bidder values are one-dimensional, bidding strategies with reasonable restrictions on bid values do not exist.