Leader-follower mean field LQ games: A direct method

This paper investigates a linear quadratic mean field game with a leader and a large number of followers. The leader first gives its strategy, and then each follower optimizes its own cost. We first solve a mean field game problem, which gives the best response of followers to the leader's strategy. After applying the followers' strategies, the leader is faced to an optimal control problem driven by a high-dimensional forward-backward stochastic differential equations (FBSDEs). By decoupling the high-dimensional Hamiltonian system with mean field approximations, we construct a set of decentralized strategies for all the players, which are further shown to be an epsilon$$ \varepsilon $$-Stackelberg equilibrium.epsilon$$ \varepsilon $$-