The article deals with the problems of mathematical modeling of social and economic systems, in which the center at the planning stage is poorly informed about the values of the parameter vector of the natural uncertainty. In contrast to the theory of active systems assumptions, the center cannot raise its level of awareness because of unobservable processes, which will occur at the stage of implementation of the decisions. The results of the conducted research are theoretical, and the proposed models and methods require detailed view of features of these systems and the available a priori information. The mathematical model developed and presented in the paper makes it possible to carry out studies that complement the well-known works about the impact of executor`s strategy on the efficiency of the system as a whole. In the study, a range of management tasks in systems with eliminated uncertainty is considered, including task planning, executor stimulation and decision analysis performed at the final stage of making and implementing decisions.