The article presents a mathematical model for the study of the equilibrium of labor resources. The problem of finding a sufficient equilibrium condition in differential games with many participants is solved. The article deals with a differential game of X persons with terminal gain, and sufficient conditions are derived in the class of positional strategies. The task is to find a sufficient equilibrium condition. The results obtained are adjacent to the results of [1,2,5], in which sufficient optimality conditions for optimal control problems and antagonistic differential games are stated.