In this work, the computational complexity of a hierarchic optimization problem involving in several players is studied. Each player is assigned with a linear objective function. The set of variables is partitioned such that each subset corresponds to one player as its decision variables. All the players jointly make a decision on the values of these variables such that a set of linear constraints should be satisfied. One special player, called the leader, makes decision on its decision variables before of all the other players. The rest, after learnt of the decision of the leader, make their choices so that their decisions form a Nash Equilibrium for them, breaking tie by maximizing the objective function of player. We show that the exact complexity of the problem is FPNP-complete.