  The large-population system consists of considerable small agents whose
individual behavior and mass effect are interrelated via their state-average.
The mean-field game provides an efficient way to get the decentralized
strategies of large-population system when studying its dynamic optimizations.
Unlike other large-population literature, this current paper possesses the
following distinctive features. First, our setting includes the partial
information structure of large-population system which is practical from real
application standpoint. Specially, two cases of partial information structure
are considered here: the partial filtration case (see Section 2, 3) where the
available information to agents is the filtration generated by an observable
component of underlying Brownian motion; the noisy observation case (Section 4)
where the individual agent can access an additive white-noise observation on
its own state. Also, it is new in filtering modeling that our sensor function
may depend on the state-average. Second, in both cases, the limiting
state-averages become random and the filtering equations to individual state
should be formalized to get the decentralized strategies. Moreover, it is also
new that the limit average of state filters should be analyzed here. This makes
our analysis very different to the full information arguments of
large-population system. Third, the consistency conditions are equivalent to
the wellposedness of some Riccati equations, and do not involve the fixed-point
analysis as in other mean-field games. The $\epsilon$-Nash equilibrium
properties are also presented.
