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A Numerical Construction Algorithm of Nash and Stackelberg Solution for Two-person Non-zero Sum Linear Positional Differential Games*. / Kleimenov, Anatolii F.; Osipov, Sergei I.; Kuvshinov, Dmitry R.
Innovations and Advances in Computer Sciences and Engineering. ed. / Tarek Sobh. Springer Netherlands, 2010. p. 249-254 Chapter 43.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Harvard

Kleimenov, AF, Osipov, SI & Kuvshinov, DR 2010, A Numerical Construction Algorithm of Nash and Stackelberg Solution for Two-person Non-zero Sum Linear Positional Differential Games*. in T Sobh (ed.), Innovations and Advances in Computer Sciences and Engineering., Chapter 43, Springer Netherlands, pp. 249-254. https://doi.org/10.1007/978-90-481-3658-2_43

APA

Kleimenov, A. F., Osipov, S. I., & Kuvshinov, D. R. (2010). A Numerical Construction Algorithm of Nash and Stackelberg Solution for Two-person Non-zero Sum Linear Positional Differential Games*. In T. Sobh (Ed.), Innovations and Advances in Computer Sciences and Engineering (pp. 249-254). [Chapter 43] Springer Netherlands. https://doi.org/10.1007/978-90-481-3658-2_43

Vancouver

Kleimenov AF, Osipov SI, Kuvshinov DR. A Numerical Construction Algorithm of Nash and Stackelberg Solution for Two-person Non-zero Sum Linear Positional Differential Games*. In Sobh T, editor, Innovations and Advances in Computer Sciences and Engineering. Springer Netherlands. 2010. p. 249-254. Chapter 43 doi: 10.1007/978-90-481-3658-2_43

Author

Kleimenov, Anatolii F. ; Osipov, Sergei I. ; Kuvshinov, Dmitry R. / A Numerical Construction Algorithm of Nash and Stackelberg Solution for Two-person Non-zero Sum Linear Positional Differential Games*. Innovations and Advances in Computer Sciences and Engineering. editor / Tarek Sobh. Springer Netherlands, 2010. pp. 249-254

BibTeX

@inproceedings{0a49ba7208984b6f8a3fa1924767b1ac,
title = "A Numerical Construction Algorithm of Nash and Stackelberg Solution for Two-person Non-zero Sum Linear Positional Differential Games*",
abstract = "The report proposes a numerical method of Stackelberg and Nash solutions construction in a class of differential games. It is based upon results of the positional antagonistic differential games theory developed by N. N. Krasovskii and his scientific school. The method transforms a non-antagonistic game into so-called non-standard optimal control problem. Numerical solutions for Stackelberg games are constructed by an algorithm developed by S. Osipov. For Nash solution construction we build auxiliary bimatrix games sequence. Both algorithms make use of known antagonistic game value computation procedures and are ultimately based upon computational geometry algorithms including convex hull construction, union, intersection, and Min-kowski sum of flat polygons. Results of numerical experiment for a material point motion in plane are presented. The point is moved by force formed by two players. Each player has his personal target point. Among the obtained results, there is a Nash solution such, that along the corresponding trajectory the position of the game is non-antagonistic at first, and then becomes globally antagonistic starting from some moment of time. {\textcopyright} Springer Science+Business Media B.V. 2010.",
author = "Kleimenov, {Anatolii F.} and Osipov, {Sergei I.} and Kuvshinov, {Dmitry R.}",
year = "2010",
doi = "10.1007/978-90-481-3658-2_43",
language = "English",
isbn = "978-90-481-3657-5",
pages = "249--254",
editor = "Tarek Sobh",
booktitle = "Innovations and Advances in Computer Sciences and Engineering",
publisher = "Springer Netherlands",
address = "Netherlands",

}

RIS

TY - GEN

T1 - A Numerical Construction Algorithm of Nash and Stackelberg Solution for Two-person Non-zero Sum Linear Positional Differential Games*

AU - Kleimenov, Anatolii F.

AU - Osipov, Sergei I.

AU - Kuvshinov, Dmitry R.

PY - 2010

Y1 - 2010

N2 - The report proposes a numerical method of Stackelberg and Nash solutions construction in a class of differential games. It is based upon results of the positional antagonistic differential games theory developed by N. N. Krasovskii and his scientific school. The method transforms a non-antagonistic game into so-called non-standard optimal control problem. Numerical solutions for Stackelberg games are constructed by an algorithm developed by S. Osipov. For Nash solution construction we build auxiliary bimatrix games sequence. Both algorithms make use of known antagonistic game value computation procedures and are ultimately based upon computational geometry algorithms including convex hull construction, union, intersection, and Min-kowski sum of flat polygons. Results of numerical experiment for a material point motion in plane are presented. The point is moved by force formed by two players. Each player has his personal target point. Among the obtained results, there is a Nash solution such, that along the corresponding trajectory the position of the game is non-antagonistic at first, and then becomes globally antagonistic starting from some moment of time. © Springer Science+Business Media B.V. 2010.

AB - The report proposes a numerical method of Stackelberg and Nash solutions construction in a class of differential games. It is based upon results of the positional antagonistic differential games theory developed by N. N. Krasovskii and his scientific school. The method transforms a non-antagonistic game into so-called non-standard optimal control problem. Numerical solutions for Stackelberg games are constructed by an algorithm developed by S. Osipov. For Nash solution construction we build auxiliary bimatrix games sequence. Both algorithms make use of known antagonistic game value computation procedures and are ultimately based upon computational geometry algorithms including convex hull construction, union, intersection, and Min-kowski sum of flat polygons. Results of numerical experiment for a material point motion in plane are presented. The point is moved by force formed by two players. Each player has his personal target point. Among the obtained results, there is a Nash solution such, that along the corresponding trajectory the position of the game is non-antagonistic at first, and then becomes globally antagonistic starting from some moment of time. © Springer Science+Business Media B.V. 2010.

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UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=84883125386

U2 - 10.1007/978-90-481-3658-2_43

DO - 10.1007/978-90-481-3658-2_43

M3 - Conference contribution

SN - 978-90-481-3657-5

SP - 249

EP - 254

BT - Innovations and Advances in Computer Sciences and Engineering

A2 - Sobh, Tarek

PB - Springer Netherlands

ER -

ID: 37853496