Mean Field Game

Mean field games (MFGs) provide a mathematical framework for analyzing the strategic interactions of a vast number of agents, approximating their collective behavior through a representative agent interacting with the average population state. Current research emphasizes developing efficient and scalable algorithms, including reinforcement learning methods and proximal point algorithms, to compute Nash equilibria in various MFG settings, particularly those with complex dynamics and population-dependent rewards. This work is significant because it addresses the computational challenges inherent in large-scale multi-agent systems, with applications ranging from energy markets and traffic flow to more general multi-agent control problems.