$ε$-Nash Equilibria for Major Minor LQG Mean Field Games with Partial Observations of All Agents
It addresses a more realistic information structure in mean field games, but the result is incremental as it extends existing theory.
This paper extends partially observed major minor LQG mean field games to general information patterns where all agents have partial observations, and establishes the existence of ε-Nash equilibria via the Separation Principle.
The partially observed major minor LQG and nonlinear mean field game (PO MM LQG MFG) systems where it is assumed the major agent's state is partially observed by each minor agent, and the major agent completely observes its own state have been analysed in the literature. In this paper, PO MM LQG MFG problems with general information patterns are studied where (i) the major agent has partial observations of its own state, and (ii) 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 a general case of indefinite 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.