A truthful learning mechanism for multi-slot sponsored search auctions with externalities

In recent years, effective sponsored search auctions (SSAs) have been designed to incentivize advertisers (advs) to bid their truthful valuations and, at the same time, to assure both the advs and the auctioneer a non–negative utility. Nonetheless, when the click–through–rates (CTRs) of the advs are unknown to the auction, these mechanisms must be paired with a learning algorithm for the estimation of the CTRs. This introduces the critical problem of designing a learning mechanism able to estimate the CTRs as the same time as implementing a truthful mechanism with a revenue loss as small as possible. In this paper, we extend previous results [2, 3] to the general case of multi–slot auctions with position– and ad–dependent externalities with particular attention on the dependency of the regret on the number of slots K and the number of advertisements n.