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Monotone numerical methods for finite-state mean-field games

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arxiv 1705.00174 v1 pith:JRBR2JA4 submitted 2017-04-29 math.NA cs.NAmath.OC

Diogo Gomes , Joao Saude This is my paper · ORCID
classification math.NAcs.NAmath.OC
keywords methodsnumericalconditionconditionsfinite-stategamesmean-fieldmfgs
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Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

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  1. A Globally Convergent Flow for Time-Dependent Mean Field Games and a Solver-Agnostic Framework for Inverse Problems

    math.OC 2026-03 conditional novelty 6.0 of 10

    A discretize-then-flow Hessian-Riemannian method globally converges for time-dependent MFGs while preserving positivity and mass, paired with a solver-agnostic bilevel inverse framework using implicit adjoint differen...

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