Game theory systems can be seen as players working together or competing to achieve goals. GPT Meets Game Theory explores a new way to understand and employ neural networks through the lens of game theory. Focusing on transformers, the engines behind today's most advanced AI, it explains key mathematical concepts and strategies in a clear, accessible way. As AI models are growing larger and taking on more data, GPT Meets Game Theory draws from biology, physics, as well as game theory, to help readers understand how we can interpret and guide the models' behavior. It also looks at how these ideas apply to "mean-field" models and how they can be used in situations like federated learning, where many devices work together to train an AI system. The book shows how choosing the right AI design and training method is like making strategic moves in a game - especially when multiple AI agents are involved. GPT Meets Game Theory offers an illuminating read for computer science, engineering, and mathematics researchers interested in the mathematical underpinnings of deep learning models, particularly transformers, and also for those who are curious about how game theory can apply to the training and optimisation of these models.