The article is dedicated to distribution of labor resources between enterprises. Allocation of labor resources in an optimal way is a difficult problem. Solving such problems may be associated with developing new theoretical and methodological approaches to constructing a system for distribution of labor resources. Economic and mathematical methods of modeling and optimization can be used to develop such systems, which will make it possible to determine the requirements for qualitative transition processes, to improve the control laws and the software implementation of the developed models. We have considered a game theory model of distribution of labor resources by enterprises based on construction of a compromise set. Employees are represented by players who evaluate their appointment with a certain positive number (the utility for the player from the assignment received ). It is believed that the utility is the greater, the more the player is satisfied with the received appointment. The utility shows the degree of satisfaction of the player's interests. Utility values for players are represented by utility matrices. The distribution of labor resources is based on construction of a compromise number. As a solution to the problem, a compromise set is proposed. The algorithm for constructing a compromise set and its time estimate are presented in the paper. A numerical example of using the described algorithm for constructing a compromise set is given. The proposed model can be used to develop a strategy for distribution of labor resources both by enterprises within the same industry, and by different industries of a certain region. Applying the simulation should allow to properly balance the costs associated with hiring and firing employees. Economic and mathematical modeling of labor resources management expands the theoretical and methodological base for study of labor resources. The representation of labor resources management in the form of a system of economic and mathematical models allow to evaluate the existing patterns in using them. We plan to automate the models we developed and create an information system for analyzing and forecasting the distribution of labor resources. Solving the problem of optimal allocation of labor resources is one of the main directions in the strategy of innovative development of Russia.