  We construct numerical approximations for Mean Field Games with fractional or
nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of
the underlying control problems/games along with dual approximations of the
distributions of agents. The methods are monotone, stable, and consistent, and
we prove convergence along subsequences for (i) degenerate equations in one
space dimension and (ii) nondegenerate equations in arbitrary dimensions. We
also give results on full convergence and convergence to classical solutions.
Numerical tests are implemented for a range of different nonlocal diffusions
and support our analytical findings.
