Lien Zoom.

We discuss infinite-horizon open-loop Nash equilibria (OLNE) in discrete-time linear-quadratic dynamic games. By embedding the dynamics into an augmented system, we show that the Riccati–Stein solution of each player coincides with that of a linear-quadratic regulator (LQR) on a lifted space. Building on this insight, we derive a finite-horizon optimal control formulation whose solutions coincide with the infinite-horizon OLNE, and reformulate it as a monotone affine variational inequality (AVI).