Mean Field Stackelberg Games: State Feedback Equilibrium

Abstract

We study mean field Stackelberg games between a major player (the leader) and a large population of minor players (the followers). By treating the mean field as part of the dynamics of the major player and a representative minor player, we Markovianize the decision problems and employ dynamic programming to determine the equilibrium strategy in a state feedback form. We show that for linear quadratic (LQ) models, the feedback equilibrium strategy is time consistent. We further give the explicit solution in a discrete-time LQ model.