The topic of this work is the relationship between the business models (BMs) of the firms which create artificial intelligence (AI) solutions in complex digital platform ecosystems and their success in profiting from innovation. The AI technology endows machines and processes with human-like communication and perception abilities, and with the capacity to learn from data and optimize at a scale not accessible to humans. The AI technology solutions depend on the underlying digital solutions for access to data and computation resources. An AI solution is a digital product offered over a complex distributed platform-based architecture that combines internal innovation with complementary assets some of which are controlled by other companies. According to the theory, external complementary assets have a substantial impact on how much a firm can profit from innovation. How key assets are allocated and controlled is part of a firm's business model. Based on a qualitative content analysis study of 170 acquired companies this work systematizes business models of AI innovators into a typology of patterns and analyzes how AI innovators of different types profit from their innovation.