In digital advertising, auctions determine the allocation of sponsored search, sponsored product, or display advertisements. The bids in these auctions for attention are largely generated by auto-bidding algorithms that are driven by platform-provided data.
We analyze the equilibrium properties of a sequence of increasingly sophisticated auto-bidding algorithms. First, we consider the equilibrium bidding behavior of an individual advertiser who controls the auto-bidding algorithm through the choice of their budget. Second, we examine the interaction when all bidders use budget-controlled bidding algorithms. Finally, we derive the bidding algorithm that maximizes the platform revenue while ensuring that all advertisers continue to participate.