Open-Loop Nash Equilibria in the Non-cooperative Infinite-planning Horizon LQ Game

J.C. Engwerda

Research output: Working paperDiscussion paperOther research output

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Abstract

Abstract: In this note we reconsider Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption that every player can stabilize the system on his own. In this note we relax this assumption and provide both necessary and sufficient conditions for existence of Nash equilibria for this game under the assumption that the system as a whole is stabilizable.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages12
Volume2012-052
Publication statusPublished - 2012

Publication series

NameCentER Discussion Paper
Volume2012-052

Fingerprint

Nash Equilibrium
Horizon
Planning
Game
Quadratic Differentials
Information Structure
Differential Games
Necessary Conditions
Sufficient Conditions
Standards

Keywords

  • linear-quadratic differential games
  • open-loop Nash equilibrium
  • solvability conditions
  • Riccati equations

Cite this

Engwerda, J. C. (2012). Open-Loop Nash Equilibria in the Non-cooperative Infinite-planning Horizon LQ Game. (CentER Discussion Paper; Vol. 2012-052). Tilburg: Econometrics.
Engwerda, J.C. / Open-Loop Nash Equilibria in the Non-cooperative Infinite-planning Horizon LQ Game. Tilburg : Econometrics, 2012. (CentER Discussion Paper).
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Engwerda, JC 2012 'Open-Loop Nash Equilibria in the Non-cooperative Infinite-planning Horizon LQ Game' CentER Discussion Paper, vol. 2012-052, Econometrics, Tilburg.

Open-Loop Nash Equilibria in the Non-cooperative Infinite-planning Horizon LQ Game. / Engwerda, J.C.

Tilburg : Econometrics, 2012. (CentER Discussion Paper; Vol. 2012-052).

Research output: Working paperDiscussion paperOther research output

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AU - Engwerda, J.C.

N1 - Pagination: 12

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N2 - Abstract: In this note we reconsider Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption that every player can stabilize the system on his own. In this note we relax this assumption and provide both necessary and sufficient conditions for existence of Nash equilibria for this game under the assumption that the system as a whole is stabilizable.

AB - Abstract: In this note we reconsider Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption that every player can stabilize the system on his own. In this note we relax this assumption and provide both necessary and sufficient conditions for existence of Nash equilibria for this game under the assumption that the system as a whole is stabilizable.

KW - linear-quadratic differential games

KW - open-loop Nash equilibrium

KW - solvability conditions

KW - Riccati equations

M3 - Discussion paper

VL - 2012-052

T3 - CentER Discussion Paper

BT - Open-Loop Nash Equilibria in the Non-cooperative Infinite-planning Horizon LQ Game

PB - Econometrics

CY - Tilburg

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Engwerda JC. Open-Loop Nash Equilibria in the Non-cooperative Infinite-planning Horizon LQ Game. Tilburg: Econometrics. 2012. (CentER Discussion Paper).