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We prove that differential Nash equilibria are generic amongst local Nashequilibria in continuous zero-sum games. That is, there exists an open-densesubset of zero-sum games for which local Nash equilibria are non-degeneratedifferential Nash equilibria. The result extends previous results to thezero-sum setting, where we obtain even stronger results; in particular, we showthat local Nash equilibria are generically hyperbolic critical points. Wefurther show that differential Nash equilibria of zero-sum games arestructurally stable. The purpose for presenting these extensions is the recentrenewed interest in zero-sum games within machine learning and optimization.Adversarial learning and generative adversarial network approaches are toutedto be more robust than the alternative. Zero-sum games are at the heart of suchapproaches. Many works proceed under the assumption of hyperbolicity ofcritical points. Our results justify this assumption by showing `almost all'zero-sum games admit local Nash equilibria that are hyperbolic.

Local Nash Equilibria are Isolated, Strict Local Nash Equilibria in `Almost All' Zero-Sum Continuous Games