Common Knowledge, Consensus, and Aggregate Information
证明，若个体后验概率的某个可容许统计量成为共同知识，则所有人的后验概率必然相同；该统计量包括随机单调函数的可逆函数。结果适用于价格等加总统计量如何传递私人信息的经济模型。
This paper investigates the effect that common knowledge of public information has on individual beliefs. We assume that n individuals start with the same prior beliefs over a finite probability space, and then each observes private information. We prove that if an admissible statistic of their posterior probabilities of an event becomes common knowledge, then everyone's posterior probabilities for that event must be the same. The class of admissible statistics includes any statistic which is an invertible function of a stochastically monotone function. We also prove that if information partitions are finite, an iterative procedure of public announcement of the statistic-where the statistic is publicly announced and then individuals recompute posterior probabilities based on their previous information plus the announced value of the statistic-converges in a finite number of steps to the common knowledge situation described above. The result has applications to asymmetric information models in economics, where private information becomes incorporated into an aggregate, publicly observed statistic such as a price or quantity in a market.