This article continues the research of the authors into cooperation between public and private investors in the natural resource sector. This work aims to analyze the partnership mechanisms in terms of efficiency, using the game-theoretical Stackelberg model. Such mechanisms determine the investment policy of the state and play an important role in addressing a whole range of issues related to the strategic management of the natural resource sector in Russia. For bilevel mathematical programming problems, the computational complexity will be evaluated and effective solution algorithms based on metaheuristics and allowing solving large-dimensional problems will be developed. This opens up the possibility of a practical study on the real data of the properties of Stackelberg equilibrium, which determines the design of the mechanism for forming investment policies. The simulation results will allow not only to assess the impact of various factors on the effectiveness of the generated subsoil development program but also to formulate the basic principles that should guide the state in the management process.