 Common Knowledge of a Multivariate Aggregate StatisticCEPR Financial Markets Paper from European Science Foundation Network in Financial Markets, c/o C.E.P.R, 33 Great Sutton Street, London EC1V 0DX. Abstract: 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. Keywords: Asymmetric Information; Common Knowledge; Stochastic Monotonicity; Rational Expectations Equilibrium (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:cpr:ceprfm:0003 Ordering information: This working paper can be ordered from Access Statistics for this paper More papers in CEPR Financial Markets Paper from European Science Foundation Network in Financial Markets, c/o C.E.P.R, 33 Great Sutton Street, London EC1V 0DX. |
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