On the noninferiority of Nash equilibrium solutions

In this paper k -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 k 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.