Beijing Institute of Mathematical Sciences and Applications

Mean-Field Games (MFG) study strategic decision-making in systems with a very large number of interacting agents, where each individual is negligible but the population as a whole shapes the environment. In this course we develop MFG theory from first principles and cover both the PDE approach and the probabilistic approach (McKean–Vlasov control, FBSDE). We will prove well-posedness results under standard monotonicity/convexity assumptions, explain the convergence from N-player Nash equilibria to MFG equilibria, and discuss extensions such as common noise, ergodic MFG, and some applications.