If a stochastically monotone function of asymmetrically informed individuals' expectations of a random vector is common knowledge, than all the individuals must agree on their expectations. This result generalizes 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 interrupted geometrically. Applied to a version of Grossman's (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.
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Paper provided by European Science Foundation Network in Financial Markets, c/o C.E.P.R, 53--56 Great Sutton Street, London EC1V 0DG in its series CEPR Financial Markets Paper with number
0003.
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