Infinite-player games where agents interact through aggregate statistics
Mean-field games (Lasry-Lions 2007, Huang-Malhamé-Caines 2006) model rational agents whose decisions depend on the population distribution. Each agent minimizes cost integrating crowd density (aversion) and distance to target (goal-seeking). At Nash equilibrium, no agent benefits from deviating. The HJB equation governs optimal control; the Fokker-Planck equation governs population evolution. Watch agents balance between reaching the goal and avoiding crowds.