Problems of management of production output in a 4-tier corporation in the face of uncertainty are investigated. There is an activity of the elements of the lower tiers of this corporation's hierarchy associated with the presence of their own objectives that do not coincide with the objectives of higher managers. These active elements may select indicators of their production outputs to maximize own objective functions, rather than the objective functions of senior executives. In case of insufficient awareness of these executives, such activity of the corporation's elements can lead to a decrease in the volume of its production. To avoid this, managers of the top two levels are advised to use training procedures based on machine learning algorithms as well as supervisor's instructions. In addition to this, the corporate production management mechanism includes rating and promotion procedures at the two lower tiers of the corporation. Depending on this mechanism, decisions of games of active elements with higher managers are determined. Sufficient conditions are found for the synthesis of such a mechanism in which the active elements of the corporation fully use their aptitude to increase the volume of production. The results obtained are illustrated by the example of a car repair management mechanism at Russian Railways.