On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийглава/раздел

Выдержка

The work is devoted to the problem of the selection of Nash equilibrium in non-cooperative differential games with an n-dimensional state variable. We consider the problem of the control harmful emissions. When solving the problem in the class of closed-loop strategies it turns out that Hamilton–Jacobi–Bellman equation may have multiple solutions. The application of an economic criterion and a classical method used in the theory of linear-quadratic regulators (LQR) to the selection of the admissible solutions from the set of obtained solutions was shown in the considered model.

Язык оригиналаанглийский
Название основной публикацииFrontiers of Dynamic Games
РедакторыLeon A. Petrosyan, Vladimir V. Mazalov, Nikolay A. Zenkevich
Место публикацииCham
ИздательBirkhäuser Verlag AG
Страницы37-48
ISBN (электронное издание)9783030236991
ISBN (печатное издание)9783030236984
DOI
СостояниеОпубликовано - 2019

Серия публикаций

НазваниеStatic and Dynamic Game Theory: Foundations and Applications
ISSN (печатное издание)2363-8516
ISSN (электронное издание)2363-8524

Предметные области Scopus

  • Теория вероятности и статистика
  • Статистика, теория вероятности и теория неопределенности
  • Прикладная математика

Цитировать

Gromova, E., & Lakhina, Y. (2019). On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control. В L. A. Petrosyan, V. V. Mazalov, & N. A. Zenkevich (Ред.), Frontiers of Dynamic Games (стр. 37-48). (Static and Dynamic Game Theory: Foundations and Applications). Cham: Birkhäuser Verlag AG. https://doi.org/10.1007/978-3-030-23699-1_3
Gromova, Ekaterina ; Lakhina, Yulia . / On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control. Frontiers of Dynamic Games. редактор / Leon A. Petrosyan ; Vladimir V. Mazalov ; Nikolay A. Zenkevich. Cham : Birkhäuser Verlag AG, 2019. стр. 37-48 (Static and Dynamic Game Theory: Foundations and Applications).
@inbook{1017644b65c24d84b09f19d346bdeeee,
title = "On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control",
abstract = "The work is devoted to the problem of the selection of Nash equilibrium in non-cooperative differential games with an n-dimensional state variable. We consider the problem of the control harmful emissions. When solving the problem in the class of closed-loop strategies it turns out that Hamilton–Jacobi–Bellman equation may have multiple solutions. The application of an economic criterion and a classical method used in the theory of linear-quadratic regulators (LQR) to the selection of the admissible solutions from the set of obtained solutions was shown in the considered model.",
keywords = "Differential games, Feedback strategies, LQR, Linear-quadratic games, Multiple solutions, Selection of Nash equilibrium",
author = "Ekaterina Gromova and Yulia Lakhina",
note = "Gromova E., Lakhina Y. (2019) On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control. In: Petrosyan L., Mazalov V., Zenkevich N. (eds) Frontiers of Dynamic Games. Static & Dynamic Game Theory: Foundations & Applications. Birkh{\"a}user, Cham",
year = "2019",
doi = "10.1007/978-3-030-23699-1_3",
language = "English",
isbn = "9783030236984",
series = "Static and Dynamic Game Theory: Foundations and Applications",
publisher = "Birkh{\"a}user Verlag AG",
pages = "37--48",
editor = "Petrosyan, {Leon A. } and Mazalov, {Vladimir V. } and Zenkevich, {Nikolay A. }",
booktitle = "Frontiers of Dynamic Games",
address = "Switzerland",

}

Gromova, E & Lakhina, Y 2019, On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control. в LA Petrosyan, VV Mazalov & NA Zenkevich (ред.), Frontiers of Dynamic Games. Static and Dynamic Game Theory: Foundations and Applications, Birkhäuser Verlag AG, Cham, стр. 37-48. https://doi.org/10.1007/978-3-030-23699-1_3

On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control. / Gromova, Ekaterina ; Lakhina, Yulia .

Frontiers of Dynamic Games. ред. / Leon A. Petrosyan; Vladimir V. Mazalov; Nikolay A. Zenkevich. Cham : Birkhäuser Verlag AG, 2019. стр. 37-48 (Static and Dynamic Game Theory: Foundations and Applications).

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийглава/раздел

TY - CHAP

T1 - On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control

AU - Gromova, Ekaterina

AU - Lakhina, Yulia

N1 - Gromova E., Lakhina Y. (2019) On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control. In: Petrosyan L., Mazalov V., Zenkevich N. (eds) Frontiers of Dynamic Games. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham

PY - 2019

Y1 - 2019

N2 - The work is devoted to the problem of the selection of Nash equilibrium in non-cooperative differential games with an n-dimensional state variable. We consider the problem of the control harmful emissions. When solving the problem in the class of closed-loop strategies it turns out that Hamilton–Jacobi–Bellman equation may have multiple solutions. The application of an economic criterion and a classical method used in the theory of linear-quadratic regulators (LQR) to the selection of the admissible solutions from the set of obtained solutions was shown in the considered model.

AB - The work is devoted to the problem of the selection of Nash equilibrium in non-cooperative differential games with an n-dimensional state variable. We consider the problem of the control harmful emissions. When solving the problem in the class of closed-loop strategies it turns out that Hamilton–Jacobi–Bellman equation may have multiple solutions. The application of an economic criterion and a classical method used in the theory of linear-quadratic regulators (LQR) to the selection of the admissible solutions from the set of obtained solutions was shown in the considered model.

KW - Differential games

KW - Feedback strategies

KW - LQR

KW - Linear-quadratic games

KW - Multiple solutions

KW - Selection of Nash equilibrium

UR - http://www.scopus.com/inward/record.url?scp=85073250595&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-23699-1_3

DO - 10.1007/978-3-030-23699-1_3

M3 - Chapter

SN - 9783030236984

T3 - Static and Dynamic Game Theory: Foundations and Applications

SP - 37

EP - 48

BT - Frontiers of Dynamic Games

A2 - Petrosyan, Leon A.

A2 - Mazalov, Vladimir V.

A2 - Zenkevich, Nikolay A.

PB - Birkhäuser Verlag AG

CY - Cham

ER -

Gromova E, Lakhina Y. On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control. В Petrosyan LA, Mazalov VV, Zenkevich NA, редакторы, Frontiers of Dynamic Games. Cham: Birkhäuser Verlag AG. 2019. стр. 37-48. (Static and Dynamic Game Theory: Foundations and Applications). https://doi.org/10.1007/978-3-030-23699-1_3