  We investigate a two-player zero-sum stochastic differential game problem
with the state process being constrained in a connected bounded closed domain,
and the cost functional described by the solution of a generalized backward
stochastic differential equation (GBSDE for short). We show that the value
functions enjoy a (strong) dynamic programming principle, and are the unique
viscosity solution of the associated Hamilton-Jacobi-Bellman-Isaacs equations
with nonlinear Neumann boundary problems. To obtain the existence for viscosity
solutions, we provide a new approach utilizing the representation theorem for
generators of the GBSDE, which is proved by a random time change method and is
a novel result in its own right.
