X Incentivized Optimal Advert Assignment via Utility Decomposition

We develop a framework for the analysis of large-scale Ad-auctions where adverts are assigned over a continuum of search types. Via a decomposition argument, the social welfare can be maximized through separate optimizations conducted by the advertisement platform and advertisers. The framework assumes a separation of time-scales, so that on each search occurrence the platform solves an assignment problem and, on a slower time scale, each advertiser varies her bid to match her demand for click-throughs with supply. By separating the problem in this way, knowledge of global parameters, such as the distribution of search terms, is not required. Exploiting the inherent information asymmetry between the platform and the advertiser, we describe a simple mechanism which implements Vickrey pricing and thus incentivizes truthful bidding. The mechanism has a unique Nash equilibrium, which maximizes social welfare. Finally, we consider models where advertisers adapt their bids smoothly over time, and prove convergence to the Nash equilibrium. The framework is flexible and tractable: we describe extensions to allow complex page layouts, reserve prices, budget constraints, and the allocation of resources across multiple keywords.