Belief Estimation by Agents in Major Minor LQG Mean Field Games

Obtaining equilibria for stochastic games where agents have independent partial (noisy) observations on the system's state, and each other's control actions, is an open area for general classes of games. This is mainly because agents' strategies may depend on mutual beliefs (estimates) of the beliefs of other agents, which may subsequently lead to an infinite regress where each agent must generate an infinite sequence of mutual beliefs. Consequently finding classes of games which have partial observations and which permit tractable solutions is of significance. In this paper, a result (CDC 2015-2016) for LQG mean field game systems consisting of one major agent and a large number of minor agents where all agents have (private) partial observations is reviewed. It is one of the rare examples of a partially observed game which has a terminating (second order) belief of belief recursion. This is followed by a Nash equilibrium result for LQG mean field game systems consisting of two major agents and a large number of minor agents, where all agents have complete observations. The nature, limitations and possible extensions of this result with partial observations for all the agents are discussed.