A fictitious-play finite-difference method for linearly solvable mean field games
Copyright policy )A fictitious-play finite-difference method for linearly solvable mean field games
An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf transformation and iterative computation using fictitious play are introduced. This leads to an implementation-friendly algorithm that iteratively solves explicit schemes. The convergence properties of the proposed scheme are mathematically proved by tracking the error of the variable through iterations. Numerical calculations show that the proposed method works stably for both one- and two-dimensional control problems.
- University of Tokyo Japan
Discrete approximations in optimal control, mean field games, Computational methods for problems pertaining to game theory, economics, and finance, Mean field games (aspects of game theory), Numerical Analysis (math.NA), Mathematics - Analysis of PDEs, PDEs in connection with game theory, economics, social and behavioral sciences, Optimization and Control (math.OC), Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mean field games and control, Mathematics - Numerical Analysis, finite difference methods, fictitious play, Mathematics - Optimization and Control, Cole-Hopf transformation, Analysis of PDEs (math.AP)
Discrete approximations in optimal control, mean field games, Computational methods for problems pertaining to game theory, economics, and finance, Mean field games (aspects of game theory), Numerical Analysis (math.NA), Mathematics - Analysis of PDEs, PDEs in connection with game theory, economics, social and behavioral sciences, Optimization and Control (math.OC), Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mean field games and control, Mathematics - Numerical Analysis, finite difference methods, fictitious play, Mathematics - Optimization and Control, Cole-Hopf transformation, Analysis of PDEs (math.AP)
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