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

Abstract

SummaryThis 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.