We outline a theory of algorithmic attention rents in digital aggregator platforms. We explore the way that as platforms grow, they become increasingly capable of extracting rents from a variety of actors in their ecosystems – users, suppliers, and advertisers – through their algorithmic control over user attention. We focus our analysis on advertising business models, in which attention harvested from users is monetized by reselling the attention to suppliers or other advertisers, though we believe the theory has relevance to other online business models as well. We argue that regulations should mandate the disclosure of the operating metrics that platforms use to allocate user attention and shape the “free” side of their marketplace, as well as details on how that attention is monetized.