02. Shiryayev V. D., Anoshchenkova E. V., Bikmurzina R. R. Teoretiko-igrovye modeli funktsionirovaniya drevovidnykh i rombovidnykh sistem upravleniya .

УДК 519.8

DOI: 10.15507/VMU.025.201501.013

GAME-THEORETIC MODELS OF TREE-STRUCTURE AND DIAMOND-STRUCTURE SYSTEMS OF MANAGEMENT FUNCTIONING

Shiryayev Viktor Dmitriyevich
(professor of Fundamental Informatics chair of Ogarev Mordovia State University (68, Bolshevistskaya Str., Saransk, Russia), Candidate of Sciences (PhD) degree holder in Physicomathematical sciences, docent, This email address is being protected from spambots. You need JavaScript enabled to view it.)

Anoshchenkova Ekaterina Vasilyevna
(lecturer of Fundamental Informatics chair of Ogarev Mordovia State University (68, Bolshevistskaya Str., Saransk, Russia), This email address is being protected from spambots. You need JavaScript enabled to view it.)

Bikmurzina Ravilya Ryashitovna
(associate professor (docent) of Fundamental Informatics chair of Ogarev Mordovia State University (68, Bolshevistskaya Str., Saransk, Russia), Candidate of Sciences (PhD) degree holder in Pedagogical sciences, This email address is being protected from spambots. You need JavaScript enabled to view it.)

Static models of hierarchical systems of management are considered in this research. The practice of creating and functioning of various organizational systems (including economic systems) shows that the process of their management should be based on the hierarchical principle. The goals of analysis and synthesis of hierarchical systems go beyond general optimal control theory, as with subsystems interacting, the very notion of optimality gets ambiguous. As a rule, the management within the scope of an economic system implies the presence of a hierarchical structure, the individual elements of which have their own goals, that could be different from the goal of the system’s development in whole. Tree-structure and diamond-structure systems of management are studied in this research. Conflict-controlled systems with hierarchical structure are added up to hierarchical games. In rather general conditions the analysis of a two-level model of hierarchical system of management comes to finding of the solution for a game. Tree-structure system of man- agement is formalized as a non-cooperative game (n+1) of a player (administrative center and operating departments В1, …, Вn). Diamond-structure system of management is formalized as a non-cooperative game with four players in its normal form. Nash equilibrium is used as a principle of optimality in a noncooperative game. Constructive methods of finding optimal solutions for these kinds of systems are provided. Multiplicity of Nash equilibria encountered is determined by dominating role of the core А0 in the game. It goes without saying that the existence of a dominant player is possible in other tasks of conflict management. In our research, however, we confine ourselves to studying tree – structure and diamond-structure system of management only.

Keywords: tree-structure system of management, diamond-structure system of management, hierarchical game, optimal strategy, Nash equilibrium, parametric programming task.

For citation: Shiryayev V. D., Anoshchenkova E. V., Bikmurzina R. R. Teoretiko-igrovye modeli funktsionirovaniya drevovidnykh i rombovidnykh sistem upravleniya [Game-theoretic models of treestructure and diamond-structure systems of management functioning]. Vestnik Mordovskogo Universiteta – Mordovia University Bulletin. 2015, vol. 25, no. 1, pp. 13–23. DOI: 10.15507/VMU.025.201501.013

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