$\epsilon$-Nash Equilibria for Major–Minor LQG Mean Field Games With Partial Observations of All Agents

Partially observed major-minor nonlinear and linear quadratic Gaussian (PO MM LQG) mean field game (MFG) systems where the major agent's state is partially observed by each minor agent, and the major agent completely observes its own state have been analyzed in the literature. In this article, PO MM LQG MFG problems with general information patterns are studied where the major agent has partial observations of its own state, and each minor agent has partial observations of its own state and the major agent's state. The assumption of partial observations by all agents leads to a new situation involving the recursive estimation by each minor agent of the major agent's estimate of its own state. For the general case of PO MM LQG MFG systems, the existence of ε-Nash equilibria, together with the individual agents' control laws yielding the equilibria, are established via the separation principle.