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This paper investigates a linear quadratic mean field leader-follower teamproblem, where the model involves one leader and a large number ofweakly-coupled interactive followers. The leader and the followers cooperate tooptimize the social cost. Specifically, for any strategy provided first by theleader, the followers would like to choose a strategy to minimize social costfunctional. Using variational analysis and person-by-person optimality, weconstruct two auxiliary control problems. By solving sequentially the auxiliarycontrol problems with consistent mean field approximations, we can obtain a setof decentralized social optimality strategy with help of a class offorward-backward consistency systems. The relevant Stackelberg equilibrium isfurther proved under some proper conditions.

Social Optima in Leader-Follower Mean Field Linear Quadratic Control