DocumentCode :
805667
Title :
On the noninferiority of Nash equilibrium solutions
Author :
Rekasius, Z.V. ; Schmitendorf, W.E.
Author_Institution :
Northwestern University, Evanston, IL, USA
Volume :
16
Issue :
2
fYear :
1971
fDate :
4/1/1971 12:00:00 AM
Firstpage :
170
Lastpage :
173
Abstract :
In this paper 
-player nonzero sum differential games are considered. A necessary condition for the closed-loop Nash equilibrium solution to be noninferior is presented. This condition involves the rank of a matrix made up of the first partial derivatives of the Hamiltonians. This condition is also a sufficient condition for the existence of a solution with the property that if the players use this solution each player does at least as well as when the Nash solutions are used and at least one player does better.
-player nonzero sum differential games are considered. A necessary condition for the closed-loop Nash equilibrium solution to be noninferior is presented. This condition involves the rank of a matrix made up of the first partial derivatives of the Hamiltonians. This condition is also a sufficient condition for the existence of a solution with the property that if the players use this solution each player does at least as well as when the Nash solutions are used and at least one player does better.Keywords :
Differential games; Control systems; Cost function; Mechanical engineering; Nash equilibrium; Partial differential equations; Sufficient conditions;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1971.1099683
Filename :
1099683
Link To Document :
