Policy Gradient Methods Find the Nash Equilibrium in N-player General-sum Linear-quadratic Games. (arXiv:2107.13090v2 [math.OC] UPDATED)

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 …

arxiv equilibrium games general gradient linear math nash equilibrium policy