The Price of Anarchy of Simultaneous First-Price Auctions with Budgets

Online advertising systems have recently transitioned to autobidding, allowing advertisers to delegate bidding decisions to automated agents. Each advertiser directs their agent to optimize an objective function subject to return-on-investment (ROI) and budget constraints. Given their practical relevance, this shift has spurred a surge of research on the liquid welfare price of anarchy (POA) of fundamental auction formats under autobidding, most notably simultaneous first-price auctions (FPA). The POA provides a worst-case efficiency guarantee that can inform format choice: it quantifies how much welfare can be lost when bidders act strategically relative to the globally optimal outcome. Determining the POA in budgeted environments has become a central objective of the recent literature in autobidding. In this talk, we present a general method to determine the price of anarchy in this setting.