Common Knowledge with Monotone Statistics
研究当个体统计量通过严格单调函数汇总时，汇总统计量的共同知识是否意味着个体统计量相等或恒定。在独立划分和关联统计两种情形下，给出了成立的条件。
When individual statistics are aggregated through a strictly monotone function to an aggregate statistic, common knowledge of the value of the aggregate statistic does not imply, in general, that the individual statistics are either equal or constant. This paper discusses circumstances where constancy and equality both hold. The first case arises when partitions are independently drawn, and each individual's information is determined by their own partition and some public signal. In this case common knowledge of the value of the aggregator function implies (with probability one) that the individual statistics are constant, so that in the case where the individual statistics have the same expected value, they must all be equal. The second circumstance is where private statistics are related: affiliation of individual statistics and a lattice condition imply that the individual statistics are equal when the value of the aggregate statistic is common knowledge.