Numerical Methods for Finite-State Mean-Field Games Satisfying a Monotonicity Condition
KAUST DepartmentApplied Mathematics and Computational Science Program
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Permanent link to this recordhttp://hdl.handle.net/10754/628842
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AbstractHere, 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 make the numerical approximation of MFGs difficult. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve both for stationary and time-dependent MFGs. We illustrate our methods with a MFG that models the paradigm-shift problem.
CitationGomes DA, Saúde J (2018) Numerical Methods for Finite-State Mean-Field Games Satisfying a Monotonicity Condition. Applied Mathematics & Optimization. Available: http://dx.doi.org/10.1007/s00245-018-9510-0.