Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential

J.C. Engwerda, Y. Salmah

Research output: Working paperDiscussion paperOther research output

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Abstract

In this note we consider the non-cooperative linear feedback Nash 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 Nash equilibrium.
Original languageEnglish
Place of PublicationTilburg
PublisherMacroeconomics
Number of pages13
Volume2010-78
Publication statusPublished - 2010

Publication series

NameCentER Discussion Paper
Volume2010-78

Fingerprint

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

Keywords

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

Cite this

Engwerda, J. C., & Salmah, Y. (2010). Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential. (CentER Discussion Paper; Vol. 2010-78). Tilburg: Macroeconomics.
Engwerda, J.C. ; Salmah, Y. / Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential. Tilburg : Macroeconomics, 2010. (CentER Discussion Paper).
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Engwerda, JC & Salmah, Y 2010 'Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential' CentER Discussion Paper, vol. 2010-78, Macroeconomics, Tilburg.

Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential. / Engwerda, J.C.; Salmah, Y.

Tilburg : Macroeconomics, 2010. (CentER Discussion Paper; Vol. 2010-78).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential

AU - Engwerda, J.C.

AU - Salmah, Y.

N1 - Pagination: 13

PY - 2010

Y1 - 2010

N2 - In this note we consider the non-cooperative linear feedback Nash 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 Nash equilibrium.

AB - In this note we consider the non-cooperative linear feedback Nash 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 Nash equilibrium.

KW - linear-quadratic games

KW - linear feedback Nash equilibrium

KW - affine systems

KW - solvability conditions

KW - Riccati equations

M3 - Discussion paper

VL - 2010-78

T3 - CentER Discussion Paper

BT - Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential

PB - Macroeconomics

CY - Tilburg

ER -

Engwerda JC, Salmah Y. Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential. Tilburg: Macroeconomics. 2010. (CentER Discussion Paper).