Balance on Nash in "soft" control problems for systems of the hierarchal type

This paper discusses the hierarchical system, which includes the Center, symbolizing the global interests of the system and control objects (CO), perform guidance Center, but at the same time pursuing its own local interests. In the first phase, the Centre produces a decision, taking into account global interests, and in the second stage CO chooses a specific version of the decision, taking into account their own administration and their local interests. It is anticipated that decision is consistent if the interests of each of the parties are counted so that a departure from it cannot improve the performance of any of the parties, i.e. it is balance on Nash. "Soft" control suggests that for each pair of "Center-facility control" global and local interests are taken into account in varying degrees. The method of finding equilibrium solutions depending on the extent of the accounting of interests and levels of reflection is found.