Efficiency of Ad Auctions with Price Displaying

Most economic reports suggest that almost half of the market value unlocked by artificial intelligence (AI) by the next decade (about 9 trillion USD per year) will be in marketing&sales. In particular, AI will allow the optimization of more and more intricate economic settings in which multiple different activities can be automated jointly. A relatively recent example is that one of ad auctions in which similar products or services are displayed together with their price, thus merging advertising and pricing in a unique website. This is the case, e.g., of Google Hotel Ads and TripAdvisor. More precisely, as in a classical ad auction, the ranking of the ads depends on the advertisers' bids, while, differently from classical ad auctions, the price is displayed together with the ad, so as to provide a direct comparison among the prices and thus dramatically affect the behavior of the users. This paper investigates how displaying prices and ads together conditions the properties of the main economic mechanisms such as VCG and GSP. Initially, we focus on the direct-revelation mechanism, showing that prices are chosen by the mechanisms once given the advertisers' reports. We also provide an efficient algorithm to compute the optimal allocation given the private information reported by the advertisers. Then, with both VCG and GSP payments, we show the inefficiency in terms of Price of Anarchy (PoA) and Stability (PoS) over the social welfare and mechanism's revenue when the advertisers choose the prices. The main results show that, with both VCG and GSP, PoS over the revenue may be unbounded even with two slots, while PoA over the social welfare may be as large as the number of slots. Finally, we show that, under some assumptions, simple modifications to VCG and GSP allow us to obtain a better PoS over the revenue.