Maximum principles for stochastic time-changed Volterra games.

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.