Common Knowledge of a Multivariate Aggregate Statistic

By Lars Tyge Nielsen

International Economic Review 36 (1995), 207-216

Abstract

If a stochastically monotone function of asymmetrically informed individuals' expectations of a random vector is common knowledge up to some observation error, then all the individuals must agree on their expectations. This result generalizes the theorem of McKelvey and Page (1986) from random variables to random vectors. It holds for general information structures given by sigma algebras.

Keywords: Asymmetric information, common knowledge, stochastic monotonicity, rational expectations equilibrium.