  We consider dynamic games defined over an infinite horizon, characterized by
linear, discrete-time dynamics and quadratic cost functionals. Considering such
linear-quadratic (LQ) dynamic games, we focus on their solutions in terms Nash
equilibrium strategies. Both Feedback (F-NE) and Open-Loop (OL-NE) Nash
equilibrium solutions are considered. The contributions of the paper are
threefold. First, our detailed study reveals some interesting structural
insights in relation to F-NE solutions. Second, as a stepping stone towards our
consideration of OL-NE strategies, we consider a specific infinite-horizon
discrete-time (single-player) optimal control problem, wherein the dynamics are
influenced by a known exogenous input and draw connections between its solution
obtained via Dynamic Programming and Pontryagin's Minimum Principle. Finally,
we exploit the latter result to provide a characterization of OL-NE strategies
of the class of infinite-horizon dynamic games. The results and key
observations made throughout the paper are illustrated via a numerical example.
