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The coal mine's undertakings in Poland have very complicated structure to managing. Therefore decision making problems in the planning and controlling of the necessaries materials are inadequate recognized. Mathematical modeling of the mining processes are today's privilege concerning of rock mass and similar problems. Application of the mathematical modeling to decision making problems in Polish coal mines however today's becomes very important. Hence we have numerous of the tests to application of the different mathematical methods supporting decision making in the coal mines. We should have to mention about the tests application of game-theory methods to decision making in coal mine industry. The game-theoretical approach to the planning and management of materials needs in the mining enterprise is presented. The hierarchical two-person non-zero-sum game was developed and justified. For the pure strategies of two persons-players (a government and its laws from one side, and a mining enterprise from another side) a game - decision selected in a form of the Stackelberg optimal strategies. A scenario of the proposed game has been verified on the example of real data from the coal mine.