  Mean Field Games provide a powerful framework to analyze the dynamics of a
large number of controlled agents in interaction. Here we consider such systems
when the interactions between agents result in a negative coordination and
analyze the behavior of the associated system of coupled PDEs using the now
well established correspondence with the non linear Schr\"odinger equation. We
focus on the long optimization time limit and on configurations such that the
game we consider goes through different regimes in which the relative
importance of disorder, interactions between agents and external potential
varies, which makes possible to get insights on the role of the
forward-backward structure of the Mean Field Game equations in relation with
the way these various regimes are connected.
