Artificial intelligence (AI) is being positioned as the defining general purpose technology of the early 21st century. Nations are racing to secure leadership in AI innovation capabilities, focusing on horizontal innovation policy to drive domestic technological competitiveness. However, the authors argue global and national administrations need to be more focused on the direction of AI innovation. They propose that a market-shaping approach can help align public and private interactions to drive AI towards advancing public interests. The authors also further propose that this requires a bolder global technology policy agenda to align and shape State and non-State actors’ relationships within AI development and diffusion towards public interest activities. They conclude with a series of limited recommendations to help policy-makers frame a market-shaping approach to AI governance.