Convex Analysis for LQG Systems with Applications to Major Minor LQG Mean-Field Game Systems
This provides a new tool for solving complex LQG mean-field game systems, avoiding restrictive assumptions needed by classical methods.
The paper develops a convex analysis approach for LQG optimal control problems that achieves an ε-Nash equilibrium in major-minor LQG mean-field game systems without imposing assumptions on mean-field evolution.
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 $ε$-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.