  In this paper, we investigate a new model of a linear-quadratic mean-field
stochastic Stackelberg differential game with one leader and two followers, in
which the leader is allowed to stop her strategy at a random time. Our
overarching goal is to find the Stackelberg solution of the leader and
followers for such a model. By employing the backward induction method, the
state equation is divided into two-stage equations. Moreover, by using the
maximum principle and the verification theorem, the Stackelberg solution is
obtained for such a model.

Optimization and Control;Functional Analysis