Infinite-Horizon Linear-Quadratic Difference Games with Coupled Affine Inequality Constraints: Open-Loop Generalized Nash Equilibria

Abstract

In this technical note, we study a class of infinite-horizon linear-quadratic difference games with coupled affine inequality constraints involving both state and control variables. We derive necessary conditions for the existence of open-loop generalized Nash equilibria and establish their sufficiency under additional assumptions. Sufficient conditions are characterized in terms of the existence of square-summable solutions to associated infinite-horizon linear complementarity systems. We further reformulate these conditions and show that computing open-loop generalized Nash equilibria reduces to solving a large-scale linear complementarity problem together with verifying additional conditions. Finally, we illustrate our results using a vehicle platooning example with constraints.