  In this paper, we obtain a null controllability result for a coupled fourth
order parabolic system based on the Stackelberg-Nash strategies. For this
purpose, we first prove the existence and uniqueness of Nash equilibrium pair
of the original system and its explicit expression is provided. Next, we
investigate the null controllability of Nash equilibrium to the corresponding
optimal system. By duality theory, we establish an observability estimate for
the coupled fourth order parabolic system. Such an estimate is obtained by a
new global Carleman estimate we derived.
