  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.
