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