Mean Field Games — Nash Crowd Equilibrium

Mean field games (Lasry-Lions 2006, Huang-Malhamé-Caines 2006) model Nash equilibria for large populations of identical rational agents. Each agent optimizes its cost, which depends on the aggregate crowd density m(x,t). The coupled HJB-Fokker-Planck system yields an equilibrium flow. Click to set a target zone.

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N agents: 200 Crowd repulsion α: 0.50 Noise σ: 0.30 Target attraction: 1.00

Agents: 200

Mean crowd cost: —

Nash condition: —

MFG system (HJB + FP):
-∂_t u + ½|∇u|² = F(x,m)
∂_t m - div(m·∇u) = σ²Δm

At equilibrium: each agent's policy is optimal given m; m is generated by those policies.

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