We present a general class of entropy-regularized multivariate LQG mean field games (MFGs) in continuous time with K distinct sub-populations of agents. We extend the notion of actions to action distributions (exploratory actions), and explicitly derive the optimal action distributions for individual agents in the limiting MFG. We demonstrate that the optimal set of action distributions yields an ϵ-Nash equilibrium for the finite-population entropy-regularized MFG. Furthermore, we compare the resulting solutions with those of classical LQG MFGs and establish the equivalence of their existence.

This is joint work with Sebastian Jaimungal.