Concerning conditions of existence of a saddle point in determinate games for integro-differential systems with a neutral type delay

The necessary conditions of the existence of a saddle point have been obtained for determinate games described by integro-differential equations of a neutral type delay or by equations unsolved for the derivative. Cases where the necessary conditions obtained are also sufficient, are indicated. It is shown that in such problems optimal controls are not, generally speaking, the saddle points of Pontryagin's function (sf. [1-4]).