On degenerate and non-degenerate correspondences of differential games with a feedback Nash equilibrium

In differential games, open-loop Nash equilibrium and feedback Nash equilibrium (FNE) are, in general, different. Only in the case of a degenerate FNE do these equilibria coincide. So far, only a countable number of games with a degenerate FNE or a non-degenerate FNE have been found. In this paper, the author shows that (i) a class of games with a degenerate FNE can be constructed from every game which has a non-degenerate FNE, and (ii) a class of games with a non-degenerate FNE can be constructed from every game which has a degenerate FNE. Hence,for any differential game with a degenerate (non-degenerate) FNE, there is a corresponding class of games which have a non-degenerate (degenerate) FNE