Eligibility Mechanisms: Auctions Meet Information Retrieval

The design of internet advertisement systems is both an auction design problem and an information retrieval (IR) problem. As an auction, the designer needs to take the participants incentives into account. As an information retrieval problem, it needs to identify the ad that it is the most relevant to a user out of an enormous set of ad candidates. Those aspects are combined by first having an IR system narrow down the initial set of ad candidates to a manageable size followed by an auction that ranks and prices those candidates. If the IR system uses information about bids, agents could in principle manipulate the system by manipulating the IR stage even when the subsequent auction is truthful. In this paper we investigate the design of truthful IR mechanisms, which we term eligibility mechanisms. We model it as a truthful version of the stochastic probing problem. We show that there is a constant gap between the truthful and non-truthful versions of the stochastic probing problem and exhibit a constant approximation algorithm. En route, we also characterize the set of eligibility mechanisms, which provides necessary and sufficient conditions for an IR system to be truthful.