  We propose projection-free sequential algorithms for linear-quadratic
dynamics games. These policy gradient based algorithms are akin to Stackelberg
leadership model and can be extended to model-free settings. We show that if
the leader performs natural gradient descent/ascent, then the proposed
algorithm has a global sublinear convergence to the Nash equilibrium. Moreover,
if the leader adopts a quasi-Newton policy, the algorithm enjoys a global
quadratic convergence. Along the way, we examine and clarify the intricacies of
adopting sequential policy updates for LQ games, namely, issues pertaining to
stabilization, indefinite cost structure, and circumventing projection steps.
