A general complex model is considered for collective dynamical strategic decision-making with explicitly interconnected factors reflecting both psychic (internal state) and behavioral (external-action, result of activity) components of agents’ activity under the given environmental and control factors. This model unifies and generalizes approaches of game theory, social psychology, theories of multi-agent systems, and control in organizational systems by simultaneous consideration of both internal and external parameters of the agents. Two special models (of informational control and informational confrontation) contain formal results on controllability and properties of equilibriums. Interpretations of a general model are conformity (threshold behavior), consensus, cognitive dissonance, and other effects with applications to production systems, multi-agent systems, crowd behavior, online social networks, and voting in small and large groups.