MEAN FIELD GAME

Crowd Dynamics — Nash Equilibrium of Interacting Agents
DENSITY ρ(x,y,t)
VELOCITY FIELD u(x,y)
0.10
0.8
150
2
Mean Field Games (Lasry-Lions 2006) model rational agents in large populations. Each agent minimizes cost including travel + congestion: ∂ₜu + ½|∇u|² = ν·Δu + γρ (HJB) coupled with ∂ₜρ − ν·Δρ − div(ρ∇u) = 0 (Fokker-Planck). The Nash equilibrium emerges from this forward-backward system. Click canvas to add a target attractor.