Mean-Field Game — Crowd Motion with Congestion

Congestion α: 2.0 Agents N: 80 Speed: 1.0 Reset Pause Single goal Two goals Circle goal

Mean-field game (Lasry-Lions 2006): each agent minimizes cost = travel time + α·∫congestion(density) dt. The Nash equilibrium is found by solving coupled Hamilton-Jacobi-Bellman (value function) and Fokker-Planck (density) PDEs. Congestion aversion spreads agents to avoid crowded paths.