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

J.C. Engwerda

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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

Keywords

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

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