Introduction to Mean-Field Games
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.
讲师
日期
2026年03月19日 至 06月04日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周四 | 14:20 - 17:50 | A3-1-301 | ZOOM 01 | 928 682 9093 | BIMSA |
修课要求
Stochastic control
课程大纲
1.Basic Stochastic Control
SDEs and Diffusion processes
Dynamic Programming Principle (DPP)
Derivation of Hamilton-Jacobi-Bellman equation
Viscosity solutions
2. Stochastic Games theory
Nash equilibrium
N-player dynamic games and associated stochastic control problems
Mean-field limit heuristic and equilibrium consistency
3.Analysis for Mean Field Games
Fokker-Planck-Hamilton-Jacobi-Bellman systems
Coupled forward–backward SDEs
Proof of the existence Theorem
Uniqueness
Application to games with finitely many players
4.Stability and continuous dependence
Stability in data/couplings
Approximation robustness
ε-Nash interpretation
5.Stationary/ergodic mean-field games
Long-time behavior; ergodic Fokker-Planck-Hamilton-Jacobi-Bellman systems
Existence issues and normalization
Links to invariant measures and control interpretation
6.Some applications to Reinforcement learning and macroeconomics
SDEs and Diffusion processes
Dynamic Programming Principle (DPP)
Derivation of Hamilton-Jacobi-Bellman equation
Viscosity solutions
2. Stochastic Games theory
Nash equilibrium
N-player dynamic games and associated stochastic control problems
Mean-field limit heuristic and equilibrium consistency
3.Analysis for Mean Field Games
Fokker-Planck-Hamilton-Jacobi-Bellman systems
Coupled forward–backward SDEs
Proof of the existence Theorem
Uniqueness
Application to games with finitely many players
4.Stability and continuous dependence
Stability in data/couplings
Approximation robustness
ε-Nash interpretation
5.Stationary/ergodic mean-field games
Long-time behavior; ergodic Fokker-Planck-Hamilton-Jacobi-Bellman systems
Existence issues and normalization
Links to invariant measures and control interpretation
6.Some applications to Reinforcement learning and macroeconomics
参考资料
J. M. Lasry, P.L.Lions, Mean field games
Carmona & Delarue, Probabilistic Theory of Mean Field Games (Vol. I–II)
Bensoussan, Frehse, Yam, Mean Field Games and Mean Field Type Control Theory
Cardaliaguet, Notes on Mean Field Games
Carmona & Delarue, Probabilistic Theory of Mean Field Games (Vol. I–II)
Bensoussan, Frehse, Yam, Mean Field Games and Mean Field Type Control Theory
Cardaliaguet, Notes on Mean Field Games
听众
Advanced Undergraduate
, Graduate
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笔记公开
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语言
中文