A two-level hierarchically organized model of managing the interaction of the director with the personnel in a company related to the development of projects in the construction sector is presented. The director acts as the leader, and the company's employees act as followers. Both management entities strive to maximize their target functions, reflecting their income and expenses. The study of the model was conducted taking into account its hierarchical structure. An algorithm for constructing a Stackelberg solution under inducement has been developed. A numerical study of the model has been conducted using the scenario method by partially enumerating the areas of admissible controls of subjects with a certain step. When conducting simulation experiments, all input parameters of the model varied in a fairly wide range. The results of the simulation experiments have been analyzed, and some patterns of system development have been identified.

Keywords: hierarchy, incentive, control system, solution algorithm, Stackelberg equilibrium, leader, follower, imitation, experiment, investment project