Policymakers increasingly recognise the need for regulatory intervention in the digital economy to promote competition, privacy and innovation, among other policy objectives. Much policy-focused literature presents regulation as a technical puzzle to be ‘solved’ through identification of the appropriate intervention in a particular context, though there is persistent disagreement among experts about what remedies are preferable in different digital markets. At the same time, many external observers emphasise the sheer multiplicity of public policy objectives that regulatory interventions might fulfil, claiming that conflicts between these objectives are inevitable and thus require political rather than technocratic solutions. This article attempts to bridge the gap between these perspectives through a novel theoretical analysis of digital markets characterised by strong network effects, conceptualising different markets in terms of common underlying structural characteristics. The resulting framework helps policymakers to anticipate which remedies will safeguard competition, privacy and innovation/efficiency under what circumstances, both in well-established digital markets and with respect to emerging technologies such as artificial intelligence. In so doing, it also highlights limits to the technocratic governance of digital markets, identifying circumstances in which conflicts between competing public values cannot be neatly resolved through technocratic regulatory intervention alone.