  Subject to reasonable conditions, in large population stochastic dynamics
games, where the agents are coupled by the system's mean field (i.e. the state
distribution of the generic agent) through their nonlinear dynamics and their
nonlinear cost functions, it can be shown that a best response control action
for each agent exists which (i) depends only upon the individual agent's state
observations and the mean field, and (ii) achieves a $\epsilon$-Nash
equilibrium for the system. In this work we formulate a class of problems where
each agent has only partial observations on its individual state. We employ
nonlinear filtering theory and the Separation Principle in order to analyze the
game in the asymptotically infinite population limit. The main result is that
the $\epsilon$-Nash equilibrium property holds where the best response control
action of each agent depends upon the conditional density of its own state
generated by a nonlinear filter, together with the system's mean field.
Finally, comparing this MFG problem with state estimation to that found in the
literature with a major agent whose partially observed state process is
independent of the control action of any individual agent, it is seen that, in
contrast, the partially observed state process of any agent in this work
depends upon that agent's control action.
