The Landscape of Auto-bidding Auctions: Value versus Utility Maximization

Internet advertisers are increasingly adopting automated bidders to buy advertising opportunities. Automated bidders simplify the procurement process by allowing advertisers to specify their goals and then bidding on their behalf in the auctions that are used to sell advertising slots. One popular goal adopted by advertisers is to maximize their clicks (or conversions) subject to a return on spend (RoS) constraint, which imposes that the ratio of total value to total spend is greater than a target ratio specified by the advertisers. The emergence of automated bidders brings into question whether the standard mechanisms used to sell ads are still effective in this new landscape. Thus motivated, in this paper, we study the problem of characterizing optimal mechanisms for selling an item to one of multiple agents with return on spend constraints when either the values or target ratios are private. We consider two objectives for the agents: value maximization, which is becoming the prevalent objective in advertising markets, and utility maximization, which is the de facto paradigm in economic theory. Our goal is to understand the impact of the agents' private information and their objectives on the seller's revenue, and determine whether the first-best revenue, which is the optimal revenue when all the private information is public, is achievable. We show that first-best revenue is achievable for value-maximizing buyers when either the target ratio or the values are private, but not when both are private. In the case of utility-maximizing buyers, first-best is never achievable and we characterize revenue-maximizing mechanisms.