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

Jacob Engwerda

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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 languageEnglish
Pages (from-to)635-656
JournalDynamic Games and Applications
Volume7
Issue number4
DOIs
Publication statusPublished - 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

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A numerical algorithm to calculate the unique feedback nash equilibrium in a large scalar LQ differential game. / Engwerda, Jacob.

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

Research output: Contribution to journalArticleScientificpeer-review

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