We develop a framework for the analysis of large-scale Ad-auctions where adverts are assigned over a con-tinuum of search types. For this pay-per-click market, we provide an efficient mechanism that maximizes social welfare. In particular, we show that the social welfare optimization can be solved in separate opti-mizations conducted on the time-scales relevant to the search platform and advertisers. Here, on each search occurrence, the platform solves an assignment problem and, on a slower time-scale, each advertiser submits a bid which matches its demand for click-throughs with supply. Importantly, knowledge of global param-eters, such as the distribution of search terms, is not required when separating the problem in this way.
Exploiting the information asymmetry between the platform and advertiser, we describe a simple mechanism which incentivizes truthful bidding and has a unique Nash equilibrium that is socially optimal, and thus implements our decomposition. Further, we consider models where advertisers adapt their bids smoothly over time, and prove convergence to the solution that maximizes social welfare. Finally, we describe several extensions which illustrate the
exibility and tractability of our framework.