Exploratory LQG Mean Field Games with Entropy Regularization

TL;DR

This paper explores entropy-regularized multi-population LQG mean field games, deriving optimal exploratory action distributions and establishing their relation to classical solutions, providing insights into equilibrium behavior.

Contribution

It extends LQG MFGs to include entropy regularization and action distributions, deriving explicit optimal strategies and connecting them to classical solutions.

Findings

Optimal action distributions are explicitly derived.

An $$-Nash equilibrium is established for finite populations.

Equivalence with classical LQG MFG solutions is demonstrated.

Abstract

We study a general class of entropy-regularized multi-variate LQG mean field games (MFGs) in continuous time with $K$ distinct sub-population 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 $\epsilon$-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.