Estimation of parameters of games with a hierarchical vector of interests
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 3, pp. 118-122
Voir la notice de l'article provenant de la source Math-Net.Ru
Many applied problems can be solved
using the methods of the game theory. One of the issues studied in
the game theory is finding of equilibrium situations, which
presuppose a preliminary determination of the values of players'
winnings.
Among the various games there are games with a hierarchical
interest vector. In such games it is assumed that a lot of players
are distributed in hierarchically organized groups. Each player
enters into several groups and allocates for each group a certain
part of his resource, which allows him to receive a certain prize.
In this case, the Nash equilibrium situation is a distribution of
the resources of all players, in which each player will receive the
maximum winnings in the game.
The problem of finding the Nash equilibrium in games with a
hierarchical vector of interests was solved by Germeyer and Vatel.
To use this theorem, it is necessary to define certain conditions
and parameters, which include, in particular, distribution of
players in hierarchically ordered groups, the evaluation of the
importance of groups for players, and the value of gains for
players.
In the work these problems are solved under the assumption
that the distribution of players into groups is carried out on the
basis of the coincidence of their goals. At the same time, to assess
the importance of groups, the hierarchy analysis method was used,
which makes it possible to give quantitative estimates based on
qualitative comparisons of the players' goals. For the construction
of the hierarchical structure of groups of players, coloured graphs
were used, the vertices of which corresponded to the players, the
edges reflected the coincidence of the goals of the players, and the
colours of the ribs made it possible to distinguish goals. The
groups of players in this case corresponded to the maximum
single-colour clicks.
Keywords:
games with a hierarchical interest vector; distribution of players into groups; assessing the importance of groups; goals of players.
@article{VYURU_2018_11_3_a8,
author = {T. V. Menshikh},
title = {Estimation of parameters of games with a hierarchical vector of interests},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
pages = {118--122},
publisher = {mathdoc},
volume = {11},
number = {3},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VYURU_2018_11_3_a8/}
}
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%0 Journal Article %A T. V. Menshikh %T Estimation of parameters of games with a hierarchical vector of interests %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie %D 2018 %P 118-122 %V 11 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/VYURU_2018_11_3_a8/ %G ru %F VYURU_2018_11_3_a8
T. V. Menshikh. Estimation of parameters of games with a hierarchical vector of interests. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 3, pp. 118-122. http://geodesic.mathdoc.fr/item/VYURU_2018_11_3_a8/