Mathematical modeling of relations between agents of an organizational system

The article discusses the main types of relationships (conflict, assistance and independence) active agents, the manifestation of which is possible when they interact in the organizational system. The agent's activity is understood as the possibility of independent goal-setting, according to which he chooses actions and his unscrupulous behavior. To characterize active agents, the concept of a utility function is introduced, which determines the agent's choice of actions that allow its usefulness to be maximized, as a rule, this is profit. The mathematical formalization of the relations of active agents is given for the option of achieving the common goal of the organizational system, as well as taking into account the achievement of local goals by active agents. To describe the interaction of active agents in the process of achieving a common goal, a matrix of the state of the organizational system is proposed, which allows to identify the existing cores of conflict, independence and assistance between active agents. The elements of the matrix are quantitative estimates of the set of agent relationships. To determine quantitative estimates of the set of agent relationships, an algorithm based on the calculation of the relative discrepancy of utility functions has been developed, which allows determining the nature and degree of agent relationships. The author's classification of agent relations according to the degree of their manifestation is proposed. An example illustrating the practical implementation of the algorithm is given.

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