  We study a stochastic differential game between two players, controlling a
forward stochastic Volterra integral equation (FSVIE). Each player has to
optimize his own performance functional which includes a backward stochastic
differential equation (BSDE). The dynamics considered are driven by
time-changed L\'evy noises, with absolutely continuous time-change process. We
prove a sufficient maximum principle to characterize Nash equilibria and the
related optimal strategies. For this we use techniques of control under partial
information, and the non-anticipating stochastic derivative. The zero-sum game
is presented as a particular case.
