论文标题
当地的纳什平衡是孤立的，严格的本地纳什均衡中的“几乎所有”零和连续游戏
Local Nash Equilibria are Isolated, Strict Local Nash Equilibria in `Almost All' Zero-Sum Continuous Games
论文作者
论文摘要
我们证明，在连续的零和游戏中，差异nash平衡是本地纳什均衡的通用。也就是说，存在一个零和游戏的开放量子集，当地的纳什均衡是非分类差分nash均衡的。该结果将先前的结果扩展到零和设置，在那里我们获得更强的结果。特别是，我们表明局部纳什平衡是一般双曲线的关键点。我们进一步表明，零和游戏的差异nash平衡在结构上是稳定的。展示这些扩展的目的是最近对机器学习和优化中零和游戏的重新兴趣。对抗性学习和生成对抗网络方法比替代方案更强大。零和游戏是这种方法的核心。许多作品在临界点的双曲性假设下进行。我们的结果证明了这一假设是合理的，显示“几乎所有”的零和游戏录入了当地的纳什均衡状态。
We prove that differential Nash equilibria are generic amongst local Nash equilibria in continuous zero-sum games. That is, there exists an open-dense subset of zero-sum games for which local Nash equilibria are non-degenerate differential Nash equilibria. The result extends previous results to the zero-sum setting, where we obtain even stronger results; in particular, we show that local Nash equilibria are generically hyperbolic critical points. We further show that differential Nash equilibria of zero-sum games are structurally stable. The purpose for presenting these extensions is the recent renewed interest in zero-sum games within machine learning and optimization. Adversarial learning and generative adversarial network approaches are touted to be more robust than the alternative. Zero-sum games are at the heart of such approaches. Many works proceed under the assumption of hyperbolicity of critical points. Our results justify this assumption by showing `almost all' zero-sum games admit local Nash equilibria that are hyperbolic.
