Convex Analysis for LQG Systems with Applications to Major Minor LQG Mean-Field Game Systems

TL;DR

This paper introduces a convex analysis method for solving LQG control problems, enabling the derivation of equilibrium strategies in major-minor mean-field games without restrictive assumptions on mean-field evolution.

Contribution

It presents a novel convex analysis framework that simplifies solving MM-LQG MFG systems and relaxes traditional assumptions on mean-field dynamics.

Findings

Derives explicit equilibrium strategies for major and minor agents.

Avoids restrictive assumptions on mean-field evolution.

Applicable to complex and non-standard systems.

Abstract

We develop a convex analysis approach for solving LQG optimal control problems and apply it to major-minor (MM) LQG mean-field game (MFG) systems. The approach retrieves the best response strategies for the major agent and all minor agents that attain an $\epsilon$-Nash equilibrium. An important and distinctive advantage to this approach is that unlike the classical approach in the literature, we are able to avoid imposing assumptions on the evolution of the mean-field. In particular, this provides a tool for dealing with complex and non-standard systems.