  This paper is devoted to a stochastic differential game of functional
forward-backward stochastic differential equation (FBSDE, for short). The
associated upper and lower value functions of the stochastic differential game
are defined by controlled functional backward stochastic differential equations
(BSDEs, for short). Applying the Girsanov transformation method introduced by
Buckdahn and Li [1], the upper and the lower value functions are shown to be
deterministic. We also generalize the Hamilton-Jacobi-Bellman-Isaacs (HJBI, for
short) equations to the path-dependent ones. By establishing the dynamic
programming principal (DPP, for short), the upper and the lower value functions
are shown to be the viscosity solutions of the corresponding upper and the
lower path-dependent HJBI equations, respectively.
