  The policy iteration method is a classical algorithm for solving optimal
control problems. In this paper, we introduce a policy iteration method for
Mean Field Games systems, and we study the convergence of this procedure to a
solution of the problem. We also introduce suitable discretizations to
numerically solve both stationary and evolutive problems. We show the
convergence of the policy iteration method for the discrete problem and we
study the performance of the proposed algorithm on some examples in dimension
one and two.
