The main applied problems that led to the emergence of the theory of differential games include the following: conflict problems of object control; control problems with uncertain interference and control problems with incomplete information. There is a connection between the conditions for the existence of equilibrium situations in game theory and the principles of analytical mechanics. Game theory finds its application in economic sciences. Thus, with the help of game theory, economists model all situations in which strategic interaction occurs. In industry market theory, games occur wherever there is more than one firm in the market.

This article presents studies of sufficient conditions for the existence of an equilibrium situation and their connection with the principle of optimality of VF Krotov. It consists in the fact that instead of finding an admissible pair of functions on which the optimality criterion reaches a minimum, a triple of functions is found, one of which is the Krotov function. This article shows that the functions used for the proof can be considered as an analogue of the Krotov function under certain conditions.