The most important when planning the development of individual regions is the question of assessing intermediate and final states. Since the development of the region is planned for a long period of time, the game-theoretic approach is possible to construct its mathematical model. A mathematical model for the development of a particular region is developed, taking into account labor movements as an investment between industries. The mathematical problem is reduced to finding the "optimal" trajectories of the development of the vector criterion of the Pareto-optimal solution. The task is to find the Pareto optimal trajectories with known vector-valued function, Nash arbitration scheme is proposed to choose as the only solution. But the Pareto-optimal set is still not enough to be able to work out a collective solution. It is necessary to determine the "fair", from the point of view of all the players, method of choosing a terminal point from the Pareto-optimal set, since only one development outcome can really be realized. For this, in the classical theory there are various arbitration schemes.