  In this note, we study a class of deterministic finite-horizon
linear-quadratic difference games with coupled-affine inequality constraints
involving both state and control variables. We show that the necessary
conditions for the existence of generalized open-loop Nash equilibria in this
game class lead to two strongly coupled discrete-time linear complementarity
systems. Subsequently, we derive the sufficient conditions by establishing an
equivalence between the solutions of these systems and the convexity of
players' objective functions. These existence conditions are then reformulated
as a solution to a linear complementarity problem, providing a numerical method
for computing these equilibria. We illustrate our results using a network flow
game with constraints.
