Monotone numerical methods for finite-state mean-field games
Numerical Analysis
2017-05-02 v1 Optimization and Control
Abstract
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.
Cite
@article{arxiv.1705.00174,
title = {Monotone numerical methods for finite-state mean-field games},
author = {Diogo Gomes and Joao Saude},
journal= {arXiv preprint arXiv:1705.00174},
year = {2017}
}