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Common Knowledge of a Multivariate Aggregate Statistic

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  • Lars Tyge Nielsen

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.

Suggested Citation

  • Lars Tyge Nielsen, 1990. "Common Knowledge of a Multivariate Aggregate Statistic," CEPR Financial Markets Paper 0003, European Science Foundation Network in Financial Markets, c/o C.E.P.R, 33 Great Sutton Street, London EC1V 0DX..
    • Handle: RePEc:cpr:ceprfm:0003
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    Cited by:

    1. Bond, Philip & Eraslan, Hülya, 2010. "Information-based trade," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1675-1703, September.
    2. Lucie Ménager, 2004. "A note on consensus and common knowledge of an aggregate of decisions," Cahiers de la Maison des Sciences Economiques v04006, Université Panthéon-Sorbonne (Paris 1).
    3. Tsakas, Elias, 2007. "Aggregate information, common knowledge, and agreeing not to bet," Working Papers in Economics 254, University of Gothenburg, Department of Economics.
    4. Ménager, Lucie, 2008. "Consensus and common knowledge of an aggregate of decisions," Games and Economic Behavior, Elsevier, vol. 62(2), pages 722-731, March.
    5. Robin Hanson, 1998. "Consensus By Identifying Extremists," Theory and Decision, Springer, vol. 44(3), pages 293-301, June.
    6. Nielsen, Lars Tyge, 1996. "Common knowledge: The case of linear regression," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 285-304.

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