Social optima in leader-follower mean field linear quadratic control

This paper investigates a linear quadratic mean field leader-follower team problem, where the model involves one leader and large number of weakly-coupled interactive followers. The followers cooperate to optimize social cost. Specifically, for any strategy provided first by leader, would like choose minimize cost functional. Using variational analysis person-by-person optimality, we construct two auxiliary control problems. By solving sequentially, problems with consistent approximations, can obtain set decentralized optimality help class forward-backward consistency systems. relevant Stackelberg equilibrium is further proved under some proper conditions.