  This paper is concerned with a non-zero sum differential game problem of an
anticipated forward-backward stochastic differential delayed equation under
partial information. We establish a necessary maximum principle and sufficient
verification theorem of the game system by virtue of the duality and convex
variational method. We apply the theoretical results and stochastic filtering
theory to study a linear-quadratic game system and derive the explicit form of
the Nash equilibrium point and discuss the existence and uniqueness in
particular cases. As an application, we consider a time-delayed pension fund
manage problem with nonlinear expectation and obtain the Nash equilibrium
point.
