Linear quadratic stackelberg difference games with constraints

In this paper we study a class of linear quadratic Stackelberg difference games with constraints. We assume that the leader has two sets of strategies. He announces only one set of strategies and the other set strategies are not announced but are constrained. We formulate the necessary conditions for the existence of Stackelberg equilibrium for this class of games. In particular, we show under a few assumptions, the necessary conditions can be recasted as a single large scale complementarity problem. We also provide sufficient conditions under which the solution of this complementarity problem is a Stackelbreg equilibrium.