  In this paper, we apply the hierarchical strategy to a semilinear weakly
degenerate parabolic equation involving a gradient term. We use the
Stackelberg-Nash strategy with one leader which tries to drive the solution to
zero and two followers intended to solve a Nash equilibrium corresponding to a
bi-objective optimal control problem. Since the system is semilinear, the
functionals are not convex in general. To overcome this difficulty, we first
prove the existence and uniqueness of the Nash quasi-equilibrium, which is a
weaker formulation of the Nash equilibrium. Next, with additional conditions,
we establish the equivalence between the Nash quasi-equilibrium and the Nash
equilibrium. We establish a suitable Carleman inequality for the adjoint system
and then an observability inequality. Based on this observability inequality,
we prove the null controllability of the linearized system. Then, due to the
Kakutani's fixed point Theorem, we obtain the null controllability of the main
system.
