Incentive compatibility is a central concept in auction theory, and a desirable property of auction mechanisms. In a celebrated result, Aggarwal, Goel and Motwani cite{AGM2006} presented the first truthful deterministic auction for sponsored search (i.e., in a setting where multiple distinct slots are auctioned). Stochastic auctions present several advantages over deterministic ones, as they are less prone to strategic bidding, and increase the diversity of the winning bidders. Meek, Chickering and Wilson cite{MCW2005} presented a family of truthful stochastic auctions for multiple identical items. %As the main result of this paper w We present the first class of incentive compatible stochastic auctions for the sponsored search setting. This class subsumes as special cases the emph{laddered} auctions of cite{AGM2006} and the stochastic auctions with the emph{condex} pricing rule of cite{MCW2005}, consolidating these two seemingly disconnected mechanisms in a single framework. Moreover, when the price per click depends deterministically on the bids the auctions in this class are unique. Accordingly, we give a precise characterization of emph{all} truthful auctions for sponsored search, in terms of the expected price that each bidder will pay per click. We also introduce randomized algorithms and pricing rules to derive, given an allocation mechanism for the single- or multiple-identical-slots scenarios, a new mechanism for the multislot framework with distinct slots. These extensions have direct practical applications.
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