The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations

J.C. Engwerda

Research output: Working paperDiscussion paperOther research output

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Abstract

In this paper we analyse the set of scalar algebraic Riccati equations (ARE) that play an important role in finding feedback Nash equilibria of the scalar N-player linear-quadratic differential game. We show that in general there exist maximal 2N - 1 solutions of the (ARE) that give rise to a Nash equilibrium. In particular we analyse the number of equilibria as a function of the state-feedback parameter and present both necessary and sufficient conditions for existence of a unique solution of the (ARE). Furthermore, we derive conditions under which the set of state-feedback parameters for which there is a unique solution grows with the number of players in the game.
Original languageEnglish
Place of PublicationTilburg
PublisherMacroeconomics
Number of pages15
Volume1999-90
Publication statusPublished - 1999

Publication series

NameCentER Discussion Paper
Volume1999-90

Fingerprint

Algebraic Riccati Equation
Solution Set
Scalar
State Feedback
Nash Equilibrium
Unique Solution
Quadratic Differentials
Differential Games
Game
Necessary Conditions
Sufficient Conditions

Keywords

  • Linear quadratic games
  • feedback Nash equilibrium
  • solvability conditions
  • Riccati equations

Cite this

Engwerda, J. C. (1999). The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations. (CentER Discussion Paper; Vol. 1999-90). Tilburg: Macroeconomics.
Engwerda, J.C. / The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations. Tilburg : Macroeconomics, 1999. (CentER Discussion Paper).
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Engwerda, JC 1999 'The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations' CentER Discussion Paper, vol. 1999-90, Macroeconomics, Tilburg.

The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations. / Engwerda, J.C.

Tilburg : Macroeconomics, 1999. (CentER Discussion Paper; Vol. 1999-90).

Research output: Working paperDiscussion paperOther research output

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Engwerda JC. The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations. Tilburg: Macroeconomics. 1999. (CentER Discussion Paper).