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

To appear in Systems & Control Letters

References in corpus (1)

• Mean-Field Leader-Follower Games with Terminal State Constraint

Cited by in corpus (4)

• $\epsilon$-Nash Equilibria for Major Minor LQG Mean Field Games with Partial Observations of All Agents
• An Overview of Some Extensions of Mean Field Games beyond Perfect Homogeneity and Anonymity
• On the Upper Bound of Near Potential Differential Games
• Mean Field Game Systems with Common Noise and Markovian Latent Processes