  The paper introduces a new approach to theory of differential games in which
entangled players try to predict and influence actions of their adversaries.
The entanglement is generated be a joint probability density known by the
players. Incase of complex density, its imaginary part represents a measure of
uncertainty of the density distribution. The novelty of the approach is in
non-Newtonian mathematical formalism thatis based upon a behavioral model of
Livings. The model is quantum-inspired: it represented by a modified Madelung
equation which the quantum potential is replaced by different, specially chosen
"computational" potential. It consists of motor dynamics simulating actual
behavior of the object, and mental dynamics representing evolution of the
corresponding knowledge-based and incorporating this knowledge in the for m of
information flows into the motor dynamics. Due to feedback from mental
dynamics, motor dynamics attains quantum-like properties: its trajectory splits
into a family of different trajectories, and each of those trajectories can be
chosen with the probability prescribed by the mental dynamics. The model
addresses a new type of entanglement that correlates the probabilities of
actions of Livings rather than the actions themselves.
