Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors

P.V. Reddy, J.C. Engwerda

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Abstract

In this article we address the problem of finding feedback Nash equilibria for linear quadratic differential games defined on descriptor systems. First, we decouple the dynamic and algebraic parts of a descriptor system using canonical projectors. We discuss the effects of feedback on the behavior of the descriptor system. We derive necessary and sufficient conditions for the existence of the feedback Nash equilibria for index 1 descriptor systems and show that there exist many informationally non-unique equilibria corresponding to a single solution of the game. Further, for descriptor systems with index greater than 1, we give a regularization based approach and discuss the associated drawbacks.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages17
Volume2010-140
Publication statusPublished - 2010

Publication series

NameCentER Discussion Paper
Volume2010-140

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Keywords

  • linear-quadratic games
  • linear feedback Nash equilibrium
  • solvability conditions
  • matrix projectors

Cite this

Reddy, P. V., & Engwerda, J. C. (2010). Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors. (CentER Discussion Paper; Vol. 2010-140). Tilburg: Econometrics.
Reddy, P.V. ; Engwerda, J.C. / Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors. Tilburg : Econometrics, 2010. (CentER Discussion Paper).
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Reddy, PV & Engwerda, JC 2010 'Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors' CentER Discussion Paper, vol. 2010-140, Econometrics, Tilburg.

Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors. / Reddy, P.V.; Engwerda, J.C.

Tilburg : Econometrics, 2010. (CentER Discussion Paper; Vol. 2010-140).

Research output: Working paperDiscussion paperOther research output

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T1 - Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors

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N2 - In this article we address the problem of finding feedback Nash equilibria for linear quadratic differential games defined on descriptor systems. First, we decouple the dynamic and algebraic parts of a descriptor system using canonical projectors. We discuss the effects of feedback on the behavior of the descriptor system. We derive necessary and sufficient conditions for the existence of the feedback Nash equilibria for index 1 descriptor systems and show that there exist many informationally non-unique equilibria corresponding to a single solution of the game. Further, for descriptor systems with index greater than 1, we give a regularization based approach and discuss the associated drawbacks.

AB - In this article we address the problem of finding feedback Nash equilibria for linear quadratic differential games defined on descriptor systems. First, we decouple the dynamic and algebraic parts of a descriptor system using canonical projectors. We discuss the effects of feedback on the behavior of the descriptor system. We derive necessary and sufficient conditions for the existence of the feedback Nash equilibria for index 1 descriptor systems and show that there exist many informationally non-unique equilibria corresponding to a single solution of the game. Further, for descriptor systems with index greater than 1, we give a regularization based approach and discuss the associated drawbacks.

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KW - linear feedback Nash equilibrium

KW - solvability conditions

KW - matrix projectors

M3 - Discussion paper

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BT - Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors

PB - Econometrics

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Reddy PV, Engwerda JC. Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors. Tilburg: Econometrics. 2010. (CentER Discussion Paper).