## $\epsilon$-Nash Equilibria for Major Minor LQG Mean Field Games with Partial Observations of All Agents. (arXiv:1810.04369v1 [math.OC])

The problems of partially observed major minor LQG and nonlinear mean field
game (PO MM LQG MFG) problems 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 the general case of indefinite LQG MFG systems,
the existence of $\epsilon$-Nash equilibria together with the individual
agents' control laws yielding the equilibria are established via the Separation
Principle.查看全文