Autobidding With Constraints

Autobidding is becoming increasingly important in the domain of online advertising, and has become a critical tool used by many advertisers for optimizing their ad campaigns. We formulate fundamental questions around the problem of bidding for performance under very general affine cost constraints. We design optimal single-agent bidding strategies for the general bidding problem, in multi-slot truthful auctions. The novel contribution is to show a strong connection between bidding and auction design, in that the bidding formula is optimal if and only if the underlying auction is truthful.Next, we move from the single-agent view to a full-system view: What happens when all advertisers adopt optimal autobidding? We prove that in general settings, there exists an equilibrium between the bidding agents for all the advertisers. As our main result, we prove a Price of Anarchy bound: For any number of general affine constraints, the total value (conversions) obtained by the advertisers in the bidding-agent equilibrium is no less than 1/2 of what we could generate via a centralized ad allocation scheme, one which does not consider any auction incentives or provide any per-advertiser guarantee.