Mean field LQG games with a major player: Continuum parameters for minor players

We consider a mean field LQG game model with a major player and a large number of minor players which are parametrized by a continuum set. We approximate the mean field generated by the minor players by a kernel representation using the Brownian motion of the major player, and local optimal control problems are solved for both the major player and a representative minor player via backward stochastic differential equations. The resulting set of decentralized control strategies based on consistent mean field approximations is shown to have an ε-Nash equilibrium property.