Auctions with Revenue Guarantees for Sponsored Search

We consider the problem of designing auctions with worst case revenue guarantees for sponsored search. This problem differs from previous work because of ad dependent clickthrough rates which lead to two natural posted-price benchmarks. In one benchmark, the winning advertisers are charged the same price per click, and in the other, the product of the price per click and the advertiser clickability (which can be thought of as the probability an advertisement is clicked if it has been seen) is the same for all winning advertisers. We adapt the random sampling auction from [10] to the sponsored search setting and improve the analysis from [1], to show a high competitive ratio for two truthful auctions, each with respect to one of the two described benchmarks. However, the two posted price benchmarks (and therefore the revenue guarantees from the corresponding random sampling auctions) can each be larger than the other; further, which is the larger cannot be determined without knowing the private values of the advertisers. We design a new auction, that incorporates these two random sampling auctions, with the following property: the auction has a Nash equilibrium; and every equilibrium has revenue at least the larger of the revenues raised by running each of the two auctions individually (assuming bidders bid truthfully when doing so is a utility maximizing strategy). Finally, we perform simulations which indicate that the revenue from our auction outperforms that from the VCG auction in less competitive markets.