The market size and strength of the major digital platform companies has invited international concern about how such firms should best be regulated to serve the interests of wider society, with a particular emphasis on the need for new anti-trust legislation. Using a normative innovation systems approach, this paper investigates how current anti-trust models may insufficiently address the value-extracting features of existing data-intensive and platform-oriented industry behaviour and business models. To do so, we employ the concept of economic rents to investigate how digital platforms create and extract value. Two forms of rent are elaborated: ‘network monopoly rents’ and ‘algorithmic rents’. By identifying such rents more precisely, policymakers and researchers can better direct regulatory investigations, as well as broader industrial and innovation policy approaches, to shape the features of platform-driven digital markets.