The paper considers possibilities of using digital technologies in the agricultural sector. It is substantiated that, along with the operational tasks of industry management, digital technologies should be aimed, first of all, at solving complex strategic problems. In a difficult and unpredictable situation in the development of the domestic agri-food market, traditional methods and tools of state regulation should be replaced by technologies and methods of artificial intelligence. The leading role among intellectual frameworks of the strategic agri-food sector management belongs to cognitive modeling. A conceptual approach to modeling strategies of agri-food market state regulation based on the construction and analysis of a fuzzy cognitive map is proposed. The purpose of strategy modeling was to study the possibilities of stimulating domestic consumer demand for food and imparting sustainable economic dynamics to agricultural production through a system of control actions based on a stabilization pricing instrument. Based on the results of the structural and target and scenario analyses of the constructed fuzzy cognitive model, the authors’ scenarios are proposed that allow substantiating the need, adequacy and efficiency of application of stimulating and regulatory managerial actions through a qualitatively new management tool.