One of the most important problems of our time is the excessive emission of carbon dioxide into the atmosphere. The article proposes a mathematical model of the system for monitoring the emission of carbon dioxide into the atmosphere. The model is two-level hierarchically organized. Industrial enterprises act as a lower-level subject of management, and the state or its authorized body acts as a top-level subject. All subjects of management of the lower level seek only to maximize their gain. The main goal of the upper level entity is to maintain the quality of atmospheric air within the specified range. The problem is considered in a game setting. The Stackelberg equilibrium is constructed. The construction algorithm is specified, and it is programmatically implemented. An analysis of the obtained results is given, a number of conclusions are made about the optimal strategies of all participants in the system, based on the results obtained in the course of applying the Stackelberg algorithm.

Keywords: Stackelberg equilibrium, two-level hierarchical model, leading, trailing, carbon dioxide, Rosprirodnadzor, Federal Service for Supervision of Natural Resources