# A numerical algorithm to calculate the unique feedback nash equilibrium in a large scalar LQ differential game

Jacob Engwerda

Research output: Contribution to journalArticleScientificpeer-review

186 Downloads (Pure)

### Abstract

In this paper, we study scalar linear quadratic differential games with state feedback information structure. We present a numerical algorithm which determines whether this game will have no, one, or multiple equilibria. Furthermore, in case there is a unique equilibrium, the algorithm provides this equilibrium. The algorithm is efficient in the sense that it is capable of handling a large number of players. The analysis is restricted to the case the involved cost depend only on the state and control variables.
Original language English 635-656 Dynamic Games and Applications 7 4 https://doi.org/10.1007/s13235-016-0201-7 Published - Dec 2017

### Fingerprint

Differential Games
Nash Equilibrium
Numerical Algorithms
Scalar
Feedback
Multiple Equilibria
Calculate
Quadratic Differentials
Information Structure
State Feedback
Game
State feedback
Costs

### Keywords

• Linear quadratic differential games
• Linear feedback Nash equilibria
• Coupled algebraic Riccati equations

### Cite this

@article{0442b2031b924be3ba607b68374d14b5,
title = "A numerical algorithm to calculate the unique feedback nash equilibrium in a large scalar LQ differential game",
abstract = "In this paper, we study scalar linear quadratic differential games with state feedback information structure. We present a numerical algorithm which determines whether this game will have no, one, or multiple equilibria. Furthermore, in case there is a unique equilibrium, the algorithm provides this equilibrium. The algorithm is efficient in the sense that it is capable of handling a large number of players. The analysis is restricted to the case the involved cost depend only on the state and control variables.",
keywords = "Linear quadratic differential games, Linear feedback Nash equilibria, Coupled algebraic Riccati equations",
author = "Jacob Engwerda",
year = "2017",
month = "12",
doi = "10.1007/s13235-016-0201-7",
language = "English",
volume = "7",
pages = "635--656",
journal = "Dynamic Games and Applications",
issn = "2153-0785",
publisher = "Springer Science + Business Media",
number = "4",

}

In: Dynamic Games and Applications, Vol. 7, No. 4, 12.2017, p. 635-656.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - A numerical algorithm to calculate the unique feedback nash equilibrium in a large scalar LQ differential game

AU - Engwerda, Jacob

PY - 2017/12

Y1 - 2017/12

N2 - In this paper, we study scalar linear quadratic differential games with state feedback information structure. We present a numerical algorithm which determines whether this game will have no, one, or multiple equilibria. Furthermore, in case there is a unique equilibrium, the algorithm provides this equilibrium. The algorithm is efficient in the sense that it is capable of handling a large number of players. The analysis is restricted to the case the involved cost depend only on the state and control variables.

AB - In this paper, we study scalar linear quadratic differential games with state feedback information structure. We present a numerical algorithm which determines whether this game will have no, one, or multiple equilibria. Furthermore, in case there is a unique equilibrium, the algorithm provides this equilibrium. The algorithm is efficient in the sense that it is capable of handling a large number of players. The analysis is restricted to the case the involved cost depend only on the state and control variables.

KW - Linear quadratic differential games

KW - Linear feedback Nash equilibria

KW - Coupled algebraic Riccati equations

U2 - 10.1007/s13235-016-0201-7

DO - 10.1007/s13235-016-0201-7

M3 - Article

VL - 7

SP - 635

EP - 656

JO - Dynamic Games and Applications

JF - Dynamic Games and Applications

SN - 2153-0785

IS - 4

ER -