Discretization of Continuum Antagonistic Game on Unit Hypercube and Transformation of Multidimensional Matrix for Solving of the Corresponding Matrix Game

Vadim V. Romanuke

doi:10.1615/JAutomatInfScien.v47.i2.80

Journal of Automation and Information Sciences

Editor chefe: Arkadiy A. Chikriy (open in a new tab)

Editor associados: Vyacheslav F. Gubarev (open in a new tab) Yuriy P. Kondratenko (open in a new tab) Nonna V. Turovyerova (open in a new tab)

Publicou 12 edições por ano

ISSN Imprimir: 1064-2315

ISSN On-line: 2163-9337

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Discretization of Continuum Antagonistic Game on Unit Hypercube and Transformation of Multidimensional Matrix for Solving of the Corresponding Matrix Game

Volume 47, Edição 2, 2015, pp. 77-86

DOI: 10.1615/JAutomatInfScien.v47.i2.80

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Vadim V. Romanuke
Khmelnitskiy National University, Khmelnitskiy

RESUMO

Method for determination of approximate solution for continuum antagonistic games on unit multidimensional cube by means of regular discretization by every dimension was proposed. To this end conditions of correct discretization of game kernel and relations, by which transformation of multidimensional matrix to linear two-dimensional one with conservation of one-one indexing of their elements, were represented. Solution of the corresponding matrix game is tested for consistency; we proposed conditions, which make it possible to evaluate variation of this solution for minimal variation of discretization step.

Palavras-chave: determination of approximate solution, continuum antagonistic game, unit multidimensional cube, regular discretization by every dimension, conditions of correct discretization of game kernel, transformation of multidimensional matrix, linear two-dimensional matrix

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