User modeling in position auctions: re-considering the GSP and VCG mechanisms

We introduce a study of position auctions, with an explicit modeling of user navigation through ads. We refer to our model as the PPA model, since it is most applicable in the context of pay-per-action position auctions. In this model, which is consistent with other recent approaches to user modeling, a typical user searches sequentially over the ordered list of ads. At each point the user has some probability of performing the action associated with the given ad, some probability of moving to the next ad, and some probability of quitting. In the framework of this model, we re-consider two basic mechanisms: the VCG position auction and the generalized second price (GSP) position auction. We study properties of these mechanisms in the context of the PPA model, and in particular show that the GSP position auction possesses a pure strategy equilibrium, and characterize a set of its equilibria. Our main corollary is that the highest revenue one may obtain in an equilibrium of the GSP position auction matches the revenue obtained in the VCG position auction. This suggests that the VCG position auction is preferable to the ad publisher upon the GSP position auction in the context of the PPA position auctions model. ∗Email: [email protected] †Email: [email protected],[email protected]