This paper reports on an experimental study of-the way in which individuals make inferences from publicly available information. We compare the predictions of a theoretical model of a common knowledge inference process with actual behavior. In the theoretical model, "perfect Bayesians," starting with private information, take actions; an aggregate statistic is made publicly available; the individuals do optimal Bayesian updating and take new actions; and the process continues until there is a common knowledge equilibrium with complete information pooling. We find that the theoretical model roughly predicts the observed behavior, but the actual inference process is clearly less efficient than the standard of the theoretical model, and while there is some pooling, it is incomplete.

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.

We provide a theorem giving a set of conditions under which public observation of an aggregate of individual expectations leads to consensus. The key concept unkerlying the result is that of common knowledge, as formalized by Aumann (1976)