Monotone numerical methods for finite-state mean-field games
This work provides a numerical approach for solving finite-state mean-field games with non-standard boundary conditions, which is a known challenge in the field.
The authors develop monotone numerical methods for finite-state mean-field games, using a monotonicity condition to construct a contraction flow whose fixed points solve the MFG. The methods are illustrated on a paradigm-shift problem.
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.