Necessary and sufficient conditions for feedback nash equilibria for the affine-quadratic differential game

J.C. Engwerda; S. Salmah

doi:10.1007%2fs10957-012-0188-1#

Necessary and sufficient conditions for feedback nash equilibria for the affine-quadratic differential game

J.C. Engwerda
, S. Salmah

Research output: Contribution to journal › Article › Scientific › peer-review

15 Citations (Scopus)

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. As a special case, we derive existence conditions for the multi-player zero-sum game.

Original language	English
Pages (from-to)	552-563
Journal	Journal of Optimization Theory and Applications
Volume	157
Issue number	2
DOIs	https://doi.org/10.1007%2fs10957-012-0188-1#
Publication status	Published - 2013

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title = "Necessary and sufficient conditions for feedback nash equilibria for the affine-quadratic differential game",

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. As a special case, we derive existence conditions for the multi-player zero-sum game.",

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AU - Salmah, S.

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N2 - 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. As a special case, we derive existence conditions for the multi-player zero-sum game.

AB - 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. As a special case, we derive existence conditions for the multi-player zero-sum game.

U2 - 10.1007%2fs10957-012-0188-1#

DO - 10.1007%2fs10957-012-0188-1#

M3 - Article

SN - 0022-3239

VL - 157

SP - 552

EP - 563

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 2

ER -

Necessary and sufficient conditions for feedback nash equilibria for the affine-quadratic differential game

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