We study mean field Stackelberg games between a major player (the leader) and a large population of minor players (the followers). By endogenizing the mean field into the system dynamics, we Markovianize the decision problems of the major player and a representative minor player and employ dynamic programming (DP) to determine the equilibrium strategy in a state feedback form. The equilibrium results from the behavior of t-selves (see e.g. Ekeland and Lazrak, 2006) labeled along time and across the population. 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.
Authors: Minyi Huang and Xuwei Yang
School of Mathematics and Statistics, Carleton University, Ottawa, Canada