Journal Article
If a stochastically monotone function of asymmetrically informed individuals expectations of a random vector is common knowledge, then all the individuals must agree on their expectations. This result generalised the theorem of Nielsen, Brandenburger, Geanakoplos, McKelvey and Page (1989) from random variables to random vectors. It holds for general information structures given by sigma-algebras. In the illustrative case of normal distributions and linear signals, it is a statement about linear algebra, and it can be interpreted geometrically. Applied to a version of Grossmans (1975, 1976, 1978) securities market model with asymmetric information, the result implies that the equilibrium price is common knowledge only if all investors agree on their conditional distributions of asset returns. Combined with a result about pooling of linear signals, this observation implies that the linear rational expectations equilibrium is unique.
