  We study a stochastic differential game between two players, controlling a
forward stochastic Volterra integral equation (FSVIE). Each player has his own
performance functional to optimize and is associated to a backward stochastic
Volterra integral equations (BSVIE). The dynamics considered are driven by
time-changed L\'evy noises with absolutely continuous time-change process. We
will then consider different information flows, techniques of control under
partial information, and the non-anticipating stochastic derivative to prove
both necessary and sufficient maximum principles to find Nash equilibria and
the related optimal strategies. We present the zero-sum game as a particular
case.
