Approximate Nash Equilibria for Discrete-Time Linear Quadratic Dynamic Games

Abstract

It is generally challenging to determine Nash equilibrium solutions of nonzero-sum dynamic games, even for games characterised by a quadratic cost and linear dynamics, and particularly in the discrete-time, infinite-horizon case. Motivated by this, we propose and characterise a notion of approximate feedback Nash equilibrium solutions for this class of dynamic games, the ϵα,β-Nash equilibrium, which provides guarantees on the convergence rate of the trajectories of the resulting closed-loop system. The efficacy of the results is demonstrated via a simulation example involving macroeconomic policy design.