| Abstract: |
| We develop a monotone-operator numerical method for a time-dependent mean field game model of price formation, coupling Hamilton--Jacobi--Bellman and transport equations with a market-clearing condition. The system is formulated as a monotone inclusion in a weak sense that encodes the forward-backward structure and boundary conditions intrinsically. A cross-assignment structure, inherited from the HJB/Fokker--Planck duality, pairs the transport residual with a spatial Sobolev preconditioner, yielding a grid-independent Lipschitz constant. We prove convergence of a projected extragradient iteration, and validate the method against an explicit benchmark for the quadratic Hamiltonian. |
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