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This paper is concerned with a non-zero sum differential game problem of ananticipated forward-backward stochastic differential delayed equation underpartial information. We establish a necessary maximum principle and sufficientverification theorem of the game system by virtue of the duality and convexvariational method. We apply the theoretical results and stochastic filteringtheory to study a linear-quadratic game system and derive the explicit form ofthe Nash equilibrium point and discuss the existence and uniqueness inparticular cases. As an application, we consider a time-delayed pension fundmanage problem with nonlinear expectation and obtain the Nash equilibriumpoint.

Non-zero sum differential games of forward-backward stochastic differential delayed equations under partial information and application