Distributed Games in Dynamic Systems: Theory, Learning, and Applications

Game theory has emerged as a fundamental framework for modeling and analyzing strategic interactions and decision-making among multiple agents, and has witnessed rapidly growing impact in cyber-physical systems over the past decade. Its integration with dynamic systems has driven major theoretical and technological advances in a wide range of applications, including smart grids, autonomous driving, robotic swarms, and networked control systems. In particular, distributed games in dynamic systems and their equilibrium learning mechanisms have attracted increasing attention due to their scalability, lightweight information exchange, and real-time implementability. This article provides a comprehensive survey of distributed games in dynamic systems, where agents interact only with local neighbors while collectively achieving global equilibrium and stability. First, the foundational theories of distributed dynamic games under three representative classes of systems: linear dynamic systems, nonlinear dynamic systems, and uncertain dynamic systems, are presented. Then, state-of-the-art distributed equilibrium learning and control methods are reviewed, including gradient-based dynamics, payoff-based learning, best-response dynamics, and learning-based approaches. To demonstrate the practical relevance and impact of distributed games in dynamic systems, representative application domains are discussed in detail. Finally, several promising future research directions are outlined, highlighting open challenges at the intersection of distributed games, learning, and dynamic systems.