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

CentER Discussion Paper Series No. 2010-78

13 Pages Posted: 30 Jul 2010  

Jacob C. Engwerda

Tilburg University - Department of Economics

Salmah

Universitas Gadjah Mada (UGM)

Date Written: July 28, 2010

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.

Keywords: linear-quadratic games, linear feedback Nash equilibrium, affine systems, solvability conditions, Riccati equations

JEL Classification: C61, C72, C73

Suggested Citation

Engwerda, Jacob C. and Salmah, Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine-Quadratic Differential Game (July 28, 2010). CentER Discussion Paper Series No. 2010-78. Available at SSRN: https://ssrn.com/abstract=1649992 or http://dx.doi.org/10.2139/ssrn.1649992

Jacob C. Engwerda (Contact Author)

Tilburg University - Department of Economics ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 2174 (Phone)
+31 13 466 3280 (Fax)

Salmah

Universitas Gadjah Mada (UGM) ( email )

Bulaksumur, Yogyakarta
Yogyakarta, Special Province of Yogyakarta
Indonesia

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