Castro等人(2009)介绍了用随机抽样逼近n人博弈的Shapley值的思想，并由Maleki(2013)等人进一步改进和Castro等人于2017年还提出了分层的方法。

The idea of approximating the Shapley value of an n-person game by random sampling was introduced by Castro et al. (2009) and further improved by Maleki et al. (2013) and Castro et al. (2017) using stratification.

与独立抽样方法相比，本文提出了一种利用一对负相关样本来减小估计方差的算法。

In contrast to their independent sampling method, in this paper, we develop an algorithm that uses a pair of negatively correlated samples to reduce the variance of the estimation.

我们测试了八个具有不同特征的博弈来测试我们提出的算法的性能。

We examine eight games with different characteristics to test the performance of our proposed algorithm.

我们表明，在大多数情况下（7/8），该方法至少具有与独立样本相似的低方差，并且在某些情况下（5/8），它显著地（平均约60%）提高了估计的质量。

We show that in most cases (seven of eight) this method has at least as low variance as an independent sample, and in some instances (five of eight), it dramatically (almost 60% on average) improves the quality of the estimation.

通过对结果的分析，我们得出结论：在边际贡献变化较大的博弈中，所推荐的方法效果最好。

After analyzing the results, we conclude that the recommended method works best in case of games with high variability in the marginal contributions.

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