标题： 玩家的效果 显示英文标题

标题： The Player's Effect

摘要： 在一个从多个参与者获取输入的函数中，一个参与者的效应衡量的是他能对该函数期望值造成的变化。 在本文中，我们证明了具有大效应的参与者数量的紧致上界，该界甚至在只知道参与者的输入是两两独立的情况下仍然成立。 我们还研究了一组参与者的效应，并表明总存在一个“小”的集合，当消除该集合后，剩下的每个集合都具有很小的效应。 最后，我们询问是否存在总是有一个具有正效应的参与者。 我们根据不同场景对这个问题给出了不同的回答，这取决于函数的性质和参与者的输入分布。 更具体地说，我们证明如果函数是非单调的，或者分布仅已知为两两独立，则可能存在所有参与者均无效应的情况。 另一方面，如果分布是具有最小支持的两两独立分布，则必然存在一个具有“大”效应的参与者。 显示英文摘要

摘要： In a function that takes its inputs from various players, the effect of a player measures the variation he can cause in the expectation of that function. In this paper we prove a tight upper bound on the number of players with large effect, a bound that holds even when the players' inputs are only known to be pairwise independent. We also study the effect of a set of players, and show that there always exists a "small" set that, when eliminated, leaves every set with little effect. Finally, we ask whether there always exists a player with positive effect. We answer this question differently in various scenarios, depending on the properties of the function and the distribution of players' inputs. More specifically, we show that if the function is non-monotone or the distribution is only known to be pairwise independent, then it is possible that all players have 0 effect. If the distribution is pairwise independent with minimal support, on the other hand, then there must exist a player with "large" effect.