论文标题
关于标准化纳什平衡的局部唯一性
On local uniqueness of normalized Nash equilibria
论文作者
论文摘要
对于具有共享约束的广义NASH均衡问题（GNEP），我们重点介绍了在非convex设置中归一化NASH平衡的概念。引入了归一化纳什平衡的非高素质的特性。非修复性是指线性独立性约束资格，严格的互补性和二阶规则性的GNEP定期版本。令人惊讶的是，标准化的纳什平衡的非平稳性并不能阻止单个玩家水平的变性。我们表明，通常所有归一化的纳什平衡都是非排定的。此外，事实证明，非平稳性是归一化纳什均衡的局部唯一性的足够条件。我们强调的是，即使在凸面中，即使在凸的概念中，非平稳性的概念与（全局）归一化nash均衡的唯一性的条件有所不同，nash均衡是从文献中知道的。
For generalized Nash equilibrium problems (GNEP) with shared constraints we focus on the notion of normalized Nash equilibrium in the nonconvex setting. The property of nondegeneracy for normalized Nash equilibria is introduced. Nondegeneracy refers to GNEP-tailored versions of linear independence constraint qualification, strict complementarity and second-order regularity. Surprisingly enough, nondegeneracy of normalized Nash equilibrium does not prevent from degeneracies at the individual players' level. We show that generically all normalized Nash equilibria are nondegenerate. Moreover, nondegeneracy turns out to be a sufficient condition for the local uniqueness of normalized Nash equilibria. We emphasize that even in the convex setting the proposed notion of nondegeneracy differs from the sufficient condition for (global) uniqueness of normalized Nash equilibria, which is known from the literature.
