Exploratory LQG mean field games with entropy regularization

We study a general class of entropy-regularized multi-variate LQG mean field game (MFG) systems in continuous time with K distinct subpopulations of agents. We extend the notion of control actions to control distributions (exploratory actions), and explicitly derive the optimal control distributions for individual agents in the limiting MFG. We demonstrate that the optimal set of control distributions yields an epsilon-Nash equilibrium for the finite-population entropy-regularized MFG. Furthermore, we compare the resulting solutions with those of classical LQG MFG systems and establish the equivalence of their existence. (C)& nbsp;2022 Elsevier Ltd. All rights reserved.