  We consider a general-sum N-player linear-quadratic game with stochastic
dynamics over a finite horizon and prove the global convergence of the natural
policy gradient method to the Nash equilibrium. In order to prove the
convergence of the method, we require a certain amount of noise in the system.
We give a condition, essentially a lower bound on the covariance of the noise
in terms of the model parameters, in order to guarantee convergence. We
illustrate our results with numerical experiments to show that even in
situations where the policy gradient method may not converge in the
deterministic setting, the addition of noise leads to convergence.
