Genericity and structural stability of non-degenerate differential Nash equilibria

We show that non-degenerate differential Nash equilibria are generic among local Nash equilibria in games with smooth costs and continuous strategy spaces, and demonstrate that such equilibria are structurally stable with respect to smooth perturbations in player costs. This implies that second-order conditions suffice to characterize local Nash equilibria in an open-dense set of games where player costs are smooth functions. Furthermore, equilibria that are computable using decoupled myopic approximate best-response persist under perturbations to the cost functions of individual players.