论文标题
Lipschitz扰动匿名游戏的常数
The Lipschitz Constant of Perturbed Anonymous Games
论文作者
论文摘要
$ n $ player $ k $ -2 $δ$ toberted Game，$λ（n，k，δ）$的最差case Lipschitz常数被赋予明确的概率描述。在$ k \ geq 3 $，$λ（n，k，δ）$的情况下，$ \ \ m athbb z $的段落概率都被标识。在$ k = 2 $和$ n $偶数的情况下，$λ（n，2，δ）$的标识是两个两个i.i.d. \二项式随机变量相等的概率。剩下的情况是$ k = 2 $和$ n $奇数，是通过相邻（偶数）$ n $的限制的。我们的表征意味着$λ（n，k，δ）$ $Δn /k \ to \ infty $的清晰闭合形式的渐近估计值。
The worst-case Lipschitz constant of an $n$-player $k$-action $δ$-perturbed game, $λ(n,k,δ)$, is given an explicit probabilistic description. In the case of $k\geq 3$, $λ(n,k,δ)$ is identified with the passage probability of a certain symmetric random walk on $\mathbb Z$. In the case of $k=2$ and $n$ even, $λ(n,2,δ)$ is identified with the probability that two two i.i.d.\ Binomial random variables are equal. The remaining case, $k=2$ and $n$ odd, is bounded through the adjacent (even) values of $n$. Our characterisation implies a sharp closed form asymptotic estimate of $λ(n,k,δ)$ as $δn /k\to\infty$.
