FEEDBACK AND OPEN-LOOP NASH EQUILIBRIA FOR LQ INFINITE-HORIZON DISCRETE-TIME DYNAMIC GAMES

We consider dynamic games defined over an infinite horizon, characterized by linear, discrete -time dynamics and quadratic cost functionals. Considering such linear -quadratic dynamic games, we focus on their solutions in terms of 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 toward 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.