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

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

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

Harvard

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

APA

Gromova, E., & Lakhina, Y. (2019). On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control. In L. A. Petrosyan, V. V. Mazalov, & N. A. Zenkevich (Eds.), Frontiers of Dynamic Games (pp. 37-48). (Static and Dynamic Game Theory: Foundations and Applications). Birkhäuser Verlag AG. https://doi.org/10.1007/978-3-030-23699-1_3

Vancouver

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

Author

Gromova, Ekaterina ; Lakhina, Yulia . / On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control. Frontiers of Dynamic Games. editor / Leon A. Petrosyan ; Vladimir V. Mazalov ; Nikolay A. Zenkevich. Cham : Birkhäuser Verlag AG, 2019. pp. 37-48 (Static and Dynamic Game Theory: Foundations and Applications).

BibTeX

@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",

}

RIS

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 -

ID: 47595167