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Original scientific paper

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

Vadim Romanuke   ORCID icon orcid.org/0000-0003-3543-3087 ; Applied Mathematics and Social Informatics Department, Khmelnitskiy National University, Khmelnitskiy, Ukraine

Fulltext: english, pdf (429 KB) pages 125-143 downloads: 117* cite
APA 6th Edition
Romanuke, V. (2014). 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, 38 (2), 125-143. Retrieved from https://hrcak.srce.hr/130816
MLA 8th Edition
Romanuke, Vadim. "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, vol. 38, no. 2, 2014, pp. 125-143. https://hrcak.srce.hr/130816. Accessed 22 Oct. 2019.
Chicago 17th Edition
Romanuke, Vadim. "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 38, no. 2 (2014): 125-143. https://hrcak.srce.hr/130816
Harvard
Romanuke, V. (2014). '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, 38(2), pp. 125-143. Available at: https://hrcak.srce.hr/130816 (Accessed 22 October 2019)
Vancouver
Romanuke V. 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 [Internet]. 2014 [cited 2019 October 22];38(2):125-143. Available from: https://hrcak.srce.hr/130816
IEEE
V. 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, vol.38, no. 2, pp. 125-143, 2014. [Online]. Available: https://hrcak.srce.hr/130816. [Accessed: 22 October 2019]

Abstracts
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.

Keywords
infinite antagonistic game; unit hypercube; sampling; multidimensional matrix; matrix game; finite support strategy; approximate solution consistency

Hrčak ID: 130816

URI
https://hrcak.srce.hr/130816

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