ИСТИНА

Quantum games so far were developed mostly as stationary or repeated games. We build truly stochastic differential dynamic games with strategies chosen by players in real time. The necessary new ingredient for quantum dynamic games is supplied by the theory of quantum filtering. Based on two versions of quantum filtering we develop quantum stochastic differential games with diffusive and counting noises. We shall show that quantum filtering allows one to reduce quantum dynamic games to stochastic differential games on complex Riemannian manifolds and provide some fully solvable examples. Quantum dynamic games represent a necessary corner stone for the theory of quantum meanfield games, developed recently bty the author.