When solving many applied problems, methods of game theory are used. In
particular, when making management decisions, it is necessary to coordinate various aspects
of decisions for which specialists in different fields are responsible. This leads to the need to
use games with non-opposing interests and finding for them Nash equilibrium. The solution
of this problem for the particular case of games with a hierarchical vector of interests is
determined by the theorem of Germeyer and Vatel. However, in proving the theorem, a
number of aspects were not taken into account. In particular, the conditions for constructing
a hierarchical tree of groups of players are undefined and the properties of the functions of
win for these groups are not fully described. In this paper, it is proposed to introduce the
concepts of player goals and, on this basis, construct a structural-parametric model of a
community of players, representing a fuzzy graph with a set of vertices corresponding to
players, and arcs reflecting the coincidence of players' goals. The weights of the arcs are
determined by the membership functions of fuzzy sets describing the significance of goals for
players. The colors of the arcs correspond to the goals of the players. After that, the concept
of a color clique is introduced and an algorithm is developed for constructing the
hierarchical structure of groups based on the successive finding of color cliques. Further,
based on the analysis of the proof of the theorem of Germeyer and Vatel, it is shown that the
function of win of a group of players must be continuous. The consequence of this is the
exclusion of cases of using discrete (in particular, integer) resources.
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Men'shikh Tatiana Valeryevna
Email: tasay94@rambler.ru
Voronezh institute of the Federal Penitentiary Service of Russia
Voronezh, Russian Federation
Novoseltsev Viktor Ivanovich
Doctor of Technical Sciences, Professor
Email: victor_novo@mail.ru
Voronezh institute of the Federal Penitentiary Service of Russia
Voronezh, Russian Federation
