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Information and $$\sigma $$ -algebras

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Listed:
  • Carlos Hervés-Beloso
  • Paulo Monteiro

Abstract

In this work, we clarify the relationship between the information that an agent receives from a signal, from an experiment or from his own ability to determine the true state of nature that occurs and the information that an agent receives from a $$\sigma $$ -algebra. We show that, for countably generated $$\sigma $$ -algebras, the larger it is, the larger the information is. The same is true for general $$\sigma $$ -algebras after the removal of a negligible set of states. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Carlos Hervés-Beloso & Paulo Monteiro, 2013. "Information and $$\sigma $$ -algebras," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 405-418, October.
    • Handle: RePEc:spr:joecth:v:54:y:2013:i:2:p:405-418
    DOI: 10.1007/s00199-012-0723-1
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    References listed on IDEAS

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    1. Carlos Hervés-Beloso & V. Martins-da-Rocha & Paulo Monteiro, 2009. "Equilibrium theory with asymmetric information and infinitely many states," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 295-320, February.
    2. 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.
    3. Dubra, Juan & Echenique, Federico, 2004. "Information is not about measurability," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 177-185, March.
    4. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Signals; Partitions; $$sigma $$ -algebras; Measurability; Information models; C60; C70;
    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

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