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This article discusses the simplest case of two economic entities competing in an antagonistic manner. The antagonism of the interaction of objects is expressed in the fact that the first object (leader) seeks to maximize the value of the residual of the parameters of the two systems, and the second to minimize it. Mathematical modeling of antagonistic interaction in an economy model with incomplete information is described by a separate set of differential equations reflecting the time change of quite a certain numerical parameter characterizing the state of an economic object at any given time, the value of which the governing body of this object seeks to increase by means available to it.