In this work, we consider linear quadratic difference games where the players face equality and inequality constraints that jointly involve the state and control variables. Although such constraints are inherently present in many applications, there are no general results available on the existence and uniqueness of equilibria in constrained linear-quadratic dynamic games (Con-LQDG). For a class of Con-LQDGs, we characterize the existence of Nash equilibria under constrained open-loop and constrained feedback information structures. In the open-loop case, we show that the existence of constrained Nash equilibrium is closely related to the solvability of a parametric two-point boundary value problem. In the feedback case, we show that the constrained feedback Nash equilibrium can be obtained from a feedback Nash equilibrium associated with an unconstrained parametric linear-quadratic game. Finally we show that the Nash equilibria, under both informational structures, are computed as solutions of a single large scale linear complementarity problem.
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