  This paper deals with a hierarchical multi-objective control problem for
forward stochastic parabolic equations with dynamic boundary conditions. The
controls are divided into two classes: leaders and followers. The goal of the
leaders is of null controllability type while the followers are in charge of
letting the state close to prescribed targets in fixed observation regions. To
solve the problem, Nash and Stackelberg strategies are used. To implement these
strategies, we combine some appropriate Carleman estimates and the well-known
control duality approach.
