Abstract. The author analyzed the method of resolving functions with regard to game theory control problems with integral constraint. A scheme of the method is proposed. This scheme ensures the end of the game within a guaranteed time in the class of stroboscopic strategies. The guaranteed times for this scheme of the resolving-functions method are compared with the results of the fiirst Pontryagin method for integral constraints .

Keywords: linear differential game, integral constraint, multi-valued mapping, measurable  selector, stroboscopic strategy.

¹ V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

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