MEAN-FIELD GAME
−∂ₜV + ½|∇V|² = ε∆V + F[m]
∂ₜm + ∇·(m∇V) = ε∆m
Agents N
300
Coupling ε
0.5
Noise σ
0.8
Target radius
0.15
Congestion cost
1.0
Reset Agents
Move Target
t:
0.0
Mean cost:
—
Near target:
—
%
Mean-field game (Lasry-Lions 2007): rational agents, Nash equilibrium in ∞-player limit. Coupled HJB + FPK equations.