  This paper is concerned with a backward-forward stochastic differential
equation (BFSDE) system, in which a large number of negligible agents are
coupled in their dynamics via state average. Here some BSDE is introduced as
the dynamics of major player, while dynamics of minor players are described by
SDEs. Some auxiliary mean-field SDEs (MFSDEs) and a $3\times2$ mixed
forward-backward stochastic differential equation (FBSDE) system are considered
and analyzed instead of involving the fixed-point analysis as in other
mean-field games. We also derive the decentralized strategies which are shown
to satisfy the $\epsilon$-Nash equilibrium property.
