Sponsored search auctions with reserve prices: Going beyond separability

The original analysis of sponsored search auctions by Varian and independently by Aggarwal et al. did not take into account the notion of reserve prices, which are common across all major search engines. We investigate this further and show that the separability assumption derived by Aggarwal et al. is not sufficient for aligning the greedy allocation employed by GSP and the efficient allocation in the presence of reserve prices. We extend separability and derive the condition under which the greedy ranking allocation is an efficient truthful mechanism. We call this generalization the extended separability condition. To complement the analysis of the extended separability condition we present an extension of the laddered auction in the presence of reserve prices, which we call the bi-laddered auction. We show that the bi-laddered auction is the unique truthful auction for advertisers that provides a price vector support for an extended GSP SNE scheme. Nevertheless the bi-laddered auction is shown to allow a budget deficit. Building on our model of reserve prices we continue by depicting advertising networks as double sided sponsored search markets with advertisers on one side, syndicators on the other, and the search engine as the market maker. For the latter model we provide a truthful scheme for the seller and show that by assuming separability one can design a SNE, individually rational, and nearly efficient syndicated market that allows the market maker (search engine) to run the market with a surplus/budget balance. The uniqueness of our bi-laddered auction scheme implies that without the separability condition no truthful syndicated market can run without a deficit.