Position auctions

I analyze the equilibria of a game based on the ad auction used by Google and Yahoo. This auction is closely related to the assignment game studied by Shapley–Shubik, Demange–Gale–Sotomayer and Roth–Sotomayer. However, due to the special structure of preferences, the equilibria of the ad auction can be calculated explicitly and some known results can be sharpened. I provide some empirical evidence that the Nash equilibria of the position auction describe the basic properties of the prices observed in Google's ad auction reasonably accurately.