Dynamic game task of executors incentives in projects for the development of new production in continuous time

The article explores the incentive problem of executors of the new products development project at the industrial enterprise in continuous time. In the process of developing new products, the learning curve effect manifests itself, which leads to a reduction in labor intensity, depending on the cumulative volume of production. The project for the new products development is considered as a managed hierarchical dynamic system, consisting of a project management board (principal) and executors (agents). The interaction of project participants is formalized as a hierarchical differential game. To solve the formulated dynamic problem of material incentives, the well-known principle of cost compensation was applied. The original problem is divided into the task of coordinated incentives and the task of coordinated planning. The study showed that the task of coordinated dynamic planning is for the principal to determine the optimal planned production volumes in order to minimize the labor cost of agents. The initial dynamic problem of material incentives was reduced to the optimal control problem. The problem of optimal control with continuous time was solved analytically using the Pontryagin maximum principle. The study identifies a condition to determine the optimal production volumes for coordination of the interests of the principal and agents.