This chapter explores the symbiotic relationship between Artificial Intelligence (AI) and trust in networked systems, focusing on how these two elements reinforce each other in strategic cybersecurity contexts. AI's capabilities in data processing, learning, and real-time response offer unprecedented support for managing trust in dynamic, complex networks. However, the successful integration of AI also hinges on the trustworthiness of AI systems themselves. Using a game-theoretic framework, this chapter presents approaches to trust evaluation, the strategic role of AI in cybersecurity, and governance frameworks that ensure responsible AI deployment. We investigate how trust, when dynamically managed through AI, can form a resilient security ecosystem. By examining trust as both an AI output and an AI requirement, this chapter sets the foundation for a positive feedback loop where AI enhances network security and the trust placed in AI systems fosters their adoption.