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Measurability Is Not about Information

Author

Listed:
  • Juan Dubra
  • Federico Echenique

    (UCLA, Berkeley, Universidad de la Republica)

Abstract

We comment on the relation between models of information based on signals/partitions, and those based on sigma-algebras. We show that more informative signals need not generate finer sigma-algebras, hence that Blackwell's theorem fails if information is modeled as sigma-algebras. The reason is that the sigma-algebra generated by a partition does not contain all the events that can be known from the information provided by the signal. We also show that there is a non-conventional sigma-algebra that can be associated to a signal which does preserve its information content. Further, expectations and conditional expectations may depend on the choice of sigma-algebra that is associated to a signal. We provide a simple characterization of when the model is robust to changes in the sigma-algebras.

Suggested Citation

  • Juan Dubra & Federico Echenique, 2001. "Measurability Is Not about Information," Cowles Foundation Discussion Papers 1296, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1296
    as

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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d12/d1296.pdf
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    References listed on IDEAS

    as
    1. Yannelis, Nicholas C, 1991. "The Core of an Economy with Differential Information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 183-197, April.
    2. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
    3. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
    4. Allen, Beth, 1983. "Neighboring information and distributions of agents' characteristics under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 12(1), pages 63-101, September.
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    Cited by:

    1. John A. Miranowski & Bruce A. Babcock, 2004. "Genetic Information in Agricultural Productivity and Product Development," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(1), pages 73-87.

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    More about this item

    Keywords

    Blackwell's theorem; measurability; models of information; partitions; information- preserving sigma-algebras;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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