An asymmetric information mean-field type linear-quadratic stochastic Stackelberg differential game with one leader and two followers

摘要

This paper is concerned with an asymmetric information linear-quadratic (AILQ) stochastic Stackelberg differential game with one leader and two followers, where the game system is governed by mean-field type stochastic differential equation (MF-SDE). With the help of two systems of Riccati equations, the followers solve a MF-type stochastic LQ game problem with partial information first, and then, the leader turns to address an optimal control problem driven by linear MF-type forward-backward stochastic differential filtering equation (MF-FBSDFE). By maximum principle, direct construction method and optimal filtering, the open-loop Stackelberg solution is expressed as a feedback form of state, state estimation, and state mean.