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In this paper, we investigate a new model of a linear-quadratic mean-fieldstochastic Stackelberg differential game with one leader and two followers, inwhich the leader is allowed to stop her strategy at a random time. Ouroverarching goal is to find the Stackelberg solution of the leader andfollowers for such a model. By employing the backward induction method, thestate equation is divided into two-stage equations. Moreover, by using themaximum principle and the verification theorem, the Stackelberg solution isobtained for such a model.

A Linear-quadratic Mean-Field Stochastic Stackelberg Differential Game with Random Exit Time