Artificial intelligence-enabled digital platforms collect and process data from and about users. These companies are largely self-regulating in Western countries. How do economic theories explain the rise of a very few dominant platforms? Mansell and Steinmueller compare and contrast neoclassical, institutional and critical political economy explanations. They show how these perspectives can lead to contrasting claims about platform benefits and harms. Uneven power relationships between platform operators and their users are treated differently in these economic traditions. Sometimes leading to advocacy for regulation or for public provision of digital services. Sometimes indicating restraint and precaution. The authors challenge the reader to think beyond the inevitability of platform dominance to create new visions of how platforms might operate in the future.