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The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations
Engwerda,J.C.
Engwerda,J.C.
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.
Description
Pagination: 15
Date
1999
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Publisher
Macroeconomics
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90.pdf
Adobe PDF, 263.22 KB
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Keywords
Linear quadratic games, feedback Nash equilibrium, solvability conditions, Riccati equations
Citation
Engwerda, J C 1999 'The Solution Set of the n-Player Scalar Feedback Nash Algebraic Riccati Equations' CentER Discussion Paper, vol. 1999-90, Macroeconomics, Tilburg.