A linear-quadratic mean-field stochastic Stackelberg differential game with random exit time

This paper is concerned with a new model of linear-quadratic mean-field stochastic Stackelberg differential game with one leader and two followers, in which only the leader is allowed to stop her strategy at a random time. By employing the backward induction method, the state equation is divided into two-stage equations. Then, the open-loop Stackelberg solution is obtained by using the maximum principle and the verification theorem. In a special case, with the help of Riccati equations, the open-loop Stackelberg solution is expressed as a feedback form of both the state and its mean.