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Currently, the theory of conflict management is in its infancy and needs further development. This is due to the emergence, presence, and development of various types of conflicts in different subject areas of the functioning of socio-economic organizations, forcing them to search for adaptive development strategies about the destructive effects of the competitive environment. The profit of organizations is characterized by the criterion of conflict stability - a dynamic trajectory of equilibrium application (a set of states) with a given efficiency. To achieve it, forecasting strategies of the behavior of competing organizations is carried out based on a variety of their considered strategies and solving the problem of rational allocation of available resources to choose the optimal one for the implementation of a given level of profit based on reducing the destructive actions of competing systems. This determines the special relevance of the task of ensuring the conflict stability of the interaction of organizations in modern conditions.
A method is proposed to substantiate the points of conflict stability of the functioning of the organizational and technical system by allocating individual and group resources for defensive and offensive actions about a structured hierarchical system of typical cores of conflict interaction between the parties.
The conducted research confirms the conclusions of well-known scientists that the stable functioning of the organizational and technical system is achievable not at the point of the minimax value of the objective function (the upper price of the game) with a priori awareness of the interacting systems, but in the form of a saddle point with a completely open game when the actions of the parties are a priori known.
A stationary equilibrium state can be asserted if, when the parameters of an organizational and technical system change as a result of the influence of external or internal disturbances, it returns to a stable equilibrium state. For a long time, only its technical elements can be in equilibrium, which does not have feedback from the external environment, whereas for the system itself, equilibrium can only be a moment in the process of continuous changes.
The process of functioning of organizational and technical systems in conditions of conflict interaction can be characterized by a mobile dynamic change in the points of stable equilibrium determined by the ability of these systems to adapt and transition to a qualitatively higher level of development. The proposed methodological approach makes it possible to find these points for various conditions of such interaction.