The rapid adoption of artificial intelligence (AI) poses new and poorly understood threats to financial stability. We use a game-theoretic model to analyse the stability impact of AI, finding that it amplifies existing financial system vulnerabilities - leverage, liquidity stress and opacity - through superior information processing, common data, speed and strategic complementarities. The consequence is crises become faster and more severe, where the likelihood of a crisis is directly affected by how effectively the authorities engage with AI. In response, we propose that the financial authorities develop their own AI systems and expertise, establish direct AI-to-AI communication, implement automated crisis facilities and monitor AI use.