This paper discusses a dynamic model of multi-agent interaction between the employing company and employees of different qualifications. The task is formalized as a game with n participants. Several employer firms simultaneously employ a finite number of employees. The usefulness of acquired employees by the firm in each separate period depends on its non-stationary utility function. It is assumed that the conditions of the game allow cooperative actions of participants and the redistribution of income between them. In addition, employee acquisition conditions may change over time. Thus, in the task of global maximization for T periods, employer firms should save some of their resources for some periods of time in order to use them in later periods of time. In this paper, an algorithm for finding a compromise solution is constructed and an example is given.