Uniqueness Conditions for the Infinite-Planning Horizon Open-Loop Linear Quadratic Differential Game

J.C. Engwerda

Research output: Working paperDiscussion paperOther research output

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Abstract

In this note we consider the open-loop Nash linear quadratic differential game with an infinite planning horizon.The performance function is assumed to be indefinite and the underlying system affine.We derive both necessary and sufficient conditions under which this game has a unique Nash equilibrium.
Original languageEnglish
Place of PublicationTilburg
PublisherMacroeconomics
Number of pages16
Volume2005-32
Publication statusPublished - 2005

Publication series

NameCentER Discussion Paper
Volume2005-32

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Quadratic Differentials
Affine Systems
Differential Games
Nash Equilibrium
Horizon
Uniqueness
Planning
Game
Necessary Conditions
Sufficient Conditions

Keywords

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

Cite this

Engwerda, J. C. (2005). Uniqueness Conditions for the Infinite-Planning Horizon Open-Loop Linear Quadratic Differential Game. (CentER Discussion Paper; Vol. 2005-32). Tilburg: Macroeconomics.
Engwerda, J.C. / Uniqueness Conditions for the Infinite-Planning Horizon Open-Loop Linear Quadratic Differential Game. Tilburg : Macroeconomics, 2005. (CentER Discussion Paper).
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Engwerda, JC 2005 'Uniqueness Conditions for the Infinite-Planning Horizon Open-Loop Linear Quadratic Differential Game' CentER Discussion Paper, vol. 2005-32, Macroeconomics, Tilburg.

Uniqueness Conditions for the Infinite-Planning Horizon Open-Loop Linear Quadratic Differential Game. / Engwerda, J.C.

Tilburg : Macroeconomics, 2005. (CentER Discussion Paper; Vol. 2005-32).

Research output: Working paperDiscussion paperOther research output

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AB - In this note we consider the open-loop Nash linear quadratic differential game with an infinite planning horizon.The performance function is assumed to be indefinite and the underlying system affine.We derive both necessary and sufficient conditions under which this game has a unique Nash equilibrium.

KW - linear-quadratic games

KW - open-loop Nash equilibrium

KW - affine systems

KW - solvability conditions

KW - Riccati equations

M3 - Discussion paper

VL - 2005-32

T3 - CentER Discussion Paper

BT - Uniqueness Conditions for the Infinite-Planning Horizon Open-Loop Linear Quadratic Differential Game

PB - Macroeconomics

CY - Tilburg

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Engwerda JC. Uniqueness Conditions for the Infinite-Planning Horizon Open-Loop Linear Quadratic Differential Game. Tilburg: Macroeconomics. 2005. (CentER Discussion Paper).