Approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix game
There is suggested a method of approximating unit-hypercubic infinite antagonistic game with the matrix game and the corresponding solution in finite strategies. The method is based on dimension-dependent irregular samplings over the game kernel. Numbers of the sampling points and their coordinates...
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University of Zagreb, Faculty of organization and informatics
2014-12-01
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doaj-a30533916c154648b2dbd209cf174dfa2021-09-02T02:16:47ZengUniversity of Zagreb, Faculty of organization and informaticsJournal of Information and Organizational Sciences1846-33121846-94182014-12-01382697Approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix gameVadim RomanukeThere is suggested a method of approximating unit-hypercubic infinite antagonistic game with the matrix game and the corresponding solution in finite strategies. The method is based on dimension-dependent irregular samplings over the game kernel. Numbers of the sampling points and their coordinates are chosen due to the stated conditions. If the sampled kernel is not the flat matrix them the multidimensional payoff matrix is reshaped into the flat one wherewith to solve the matrix game. The reshaping is a reversible matrix map. The concluding step of the approximation is in checking the finite solution consistency. Consistency can be weakened, and consistency can be checked at some rank corresponding to a natural number. The higher rank of the finite solution consistency is, the wider neighborhood of the sampling numbers at which the solution properties are monotonic-like.http://jios.foi.hr/index.php/jios/article/view/897infinite antagonistic gameunit hypercubesamplingmultidimensional matrixmatrix gamefinite support strategyapproximate solution consistency |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Vadim Romanuke |
spellingShingle |
Vadim Romanuke Approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix game Journal of Information and Organizational Sciences infinite antagonistic game unit hypercube sampling multidimensional matrix matrix game finite support strategy approximate solution consistency |
author_facet |
Vadim Romanuke |
author_sort |
Vadim Romanuke |
title |
Approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix game |
title_short |
Approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix game |
title_full |
Approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix game |
title_fullStr |
Approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix game |
title_full_unstemmed |
Approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix game |
title_sort |
approximation of unit-hypercubic infinite antagonistic game via dimension-dependent irregular samplings and reshaping the payoffs into flat matrix wherewith to solve the matrix game |
publisher |
University of Zagreb, Faculty of organization and informatics |
series |
Journal of Information and Organizational Sciences |
issn |
1846-3312 1846-9418 |
publishDate |
2014-12-01 |
description |
There is suggested a method of approximating unit-hypercubic infinite antagonistic game with the matrix game and the corresponding solution in finite strategies. The method is based on dimension-dependent irregular samplings over the game kernel. Numbers of the sampling points and their coordinates are chosen due to the stated conditions. If the sampled kernel is not the flat matrix them the multidimensional payoff matrix is reshaped into the flat one wherewith to solve the matrix game. The reshaping is a reversible matrix map. The concluding step of the approximation is in checking the finite solution consistency. Consistency can be weakened, and consistency can be checked at some rank corresponding to a natural number. The higher rank of the finite solution consistency is, the wider neighborhood of the sampling numbers at which the solution properties are monotonic-like. |
topic |
infinite antagonistic game unit hypercube sampling multidimensional matrix matrix game finite support strategy approximate solution consistency |
url |
http://jios.foi.hr/index.php/jios/article/view/897 |
work_keys_str_mv |
AT vadimromanuke approximationofunithypercubicinfiniteantagonisticgameviadimensiondependentirregularsamplingsandreshapingthepayoffsintoflatmatrixwherewithtosolvethematrixgame |
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1721181502147919872 |