均衡策略的经验分布及其检验应用
Empirical Distribution of Equilibrium Play and Its Testing Application
摘要：
我们表明，在任何$n$ -玩家$m$ -动作规范型博弈中，我们可以通过对任何混合动作均衡进行少量采样来获得近似均衡。我们研究了三种类型的均衡：纳什均衡，相关和粗糙相关。对于其中的每一个，我们得到的样本数量的上限和下限的经验分布所需的采样动作配置文件，以形成一个近似的平衡概率接近一。这些界限意味着，即使在$n$和$m$都很大的博弈中，我们也可以使用少量样本来检验参与者是否按照近似均衡进行博弈。此外，我们的研究结果大大提高了以前已知的上界的支持大小的近似均衡在游戏中有许多球员。特别是，对于所有的三种类型的平衡，我们证明了存在的近似平衡与支持大小polylogarian在$n$和$m$，而以前最有名的上限是多项式在$n$。
英文摘要：
We show that in any $n$-player $m$-action normal-form game, we can obtain an approximate equilibrium by sampling any mixed-action equilibrium a small number of times. We study three types of equilibria: Nash, correlated and coarse correlated. For each one of them we obtain upper and lower bounds on the number of samples required for the empirical distribution over the sampled action profiles to form an approximate equilibrium with probability close to one. These bounds imply that using a small number of samples we can test whether or not players are playing according to an approximate equilibrium, even in games where $n$ and $m$ are large. In addition, our results substantially improve previously known upper bounds on the support size of approximate equilibria in games with many players. In particular, for all the three types of equilibria we show the existence of approximate equilibrium with support size polylogarithmic in $n$ and $m$, whereas the previously best-known upper bounds were polynomial in $n$.
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