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A redistribution system is any social system as organization, company or institution is where the redistribution of payments of players in comparison with their performance happens. The very important role is played by constitutions of alliances created in this system. Modeling of essential three players redistribution system as well as identifying and calculating the forms of equilibrium (discriminatory or Nash) provide the key for analysis of a real individual or group behavior including problems of its stability and chaining of other social systems. The theory of redistribution systems, as an original extension, comes out of the “game theory” and it has numerous practical applications.