In this paper we study a class of N -player finite-horizon linear-quadratic difference games with linear constraints. We introduce a specific information structure and derive necessary conditions for the existence of open-loop and closed-loop (no-memory) Nash equilibria. We show that these conditions lead to a weakly coupled system of parametric two-point boundary-value problem and a set of linear-complementarity problems. Further, under certain assumptions we show that these necessary conditions can be reformulated as a single large-scale parametric linear-complementarity problem. We illustrate our results with a numerical example.