An original mathematical model describing different activities of actors in the vertical marketing system is presented. They are a provider, a agent, a trading enterprise are presented as a controlling subjects. The model is based on the game-theoretical and hierarchical approach. An equilibrium of Germeyer G1 game in terms of sustainable development is established. The method of impulsion is used as a method of hierarchical control to solve this model. The main system operation laws based on numerical experiments are presented.

Keywords: game theory, hierarchical, three-level control system, method of impulsion