A FULLY DISCRETE SEMI-LAGRANGIAN SCHEME FOR A FIRST ORDER MEAN FIELD GAME PROBLEM

A FULLY DISCRETE SEMI-LAGRANGIAN SCHEME FOR A FIRST ORDER MEAN FIELD GAME PROBLEM

In this work we propose a fully discrete semi-Lagrangian scheme for a first order mean field game system. We prove that the resulting discretization admits at least one solution and, in the scalar case, we prove a convergence result for the scheme. Numerical simulations and examples are also discuss...

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Veröffentlicht in:SIAM journal on numerical analysis 2014-01, Vol.52 (1), p.45-67
Hauptverfasser: CARLINI, E., SILVA, F. J.
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Approximation
Computer simulation
Continuity equations
Density
Error rates
Games
Mass distribution
Mathematical functions
Mathematics
Numerical analysis
Numerical methods
Optimization and Control
Uniqueness
Viscosity
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Zusammenfassung:In this work we propose a fully discrete semi-Lagrangian scheme for a first order mean field game system. We prove that the resulting discretization admits at least one solution and, in the scalar case, we prove a convergence result for the scheme. Numerical simulations and examples are also discussed.
ISSN:0036-1429
1095-7170
DOI:10.1137/120902987