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

J.C. Engwerda, S. Salmah

Research output: Contribution to journalArticleScientificpeer-review

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 languageEnglish
Pages (from-to)552-563
JournalJournal of Optimization Theory and Applications
Volume157
Issue number2
DOIs
Publication statusPublished - 2013

Fingerprint

Quadratic Differentials
Differential Games
Nash Equilibrium
Feedback
Necessary Conditions
Planning
Affine Systems
Zero sum game
Sufficient Conditions
Horizon
Game
Nash equilibrium
Differential games
Zero-sum game

Cite this

@article{f96765515d124ecd848a5511bb6f314b,
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.",
author = "J.C. Engwerda and S. Salmah",
year = "2013",
doi = "10.1007{\%}2fs10957-012-0188-1#",
language = "English",
volume = "157",
pages = "552--563",
journal = "Journal of Optimization Theory and Applications",
issn = "0022-3239",
publisher = "SPRINGER/PLENUM PUBLISHERS",
number = "2",

}

Necessary and sufficient conditions for feedback nash equilibria for the affine-quadratic differential game. / Engwerda, J.C.; Salmah, S.

In: Journal of Optimization Theory and Applications, Vol. 157, No. 2, 2013, p. 552-563.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Necessary and sufficient conditions for feedback nash equilibria for the affine-quadratic differential game

AU - Engwerda, J.C.

AU - Salmah, S.

PY - 2013

Y1 - 2013

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

VL - 157

SP - 552

EP - 563

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

IS - 2

ER -