Monotone numerical methods for finite-state mean-field games

2017/04/29 by Gomes, Diogo, Saude, Joao
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1705.00174

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.

Related

• An introduction to monotonicity methods in mean-field games
• Two numerical approaches to stationary mean-field games
• Mean Field Games of Controls: Finite Difference Approximations
• Solving Mean-Field Games with Monotonicity Methods in Banach Spaces
• Monotone solutions to mean field games master equation in the L2-monotone setting