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Information and the dispersion of posterior expectations

Author

Listed:
  • Brandt, Nikolai
  • Drees, Burkhard
  • Eckwert, Bernhard
  • Várdy, Felix

Abstract

We explore the intuitive idea that more information leads to greater dispersion of posterior beliefs about the expected state of the world. First, we show that two dispersion orders that have been widely used as informativeness criteria do not satisfy the desirable property of ordinality of states (OS), i.e., invariance to increasing monotone state transformations. Then, for the class of monotone information systems, we characterize the weakest information criteria that respect OS and imply the dispersion orders. Our characterizations consist of intuitive conditions on the joint distributions of signals and states. Because of OS, the information criteria induce the dispersion orders not only on the posterior expectations of states, but also of state utilities, under any strictly increasing vNM utility function.

Suggested Citation

  • Brandt, Nikolai & Drees, Burkhard & Eckwert, Bernhard & Várdy, Felix, 2014. "Information and the dispersion of posterior expectations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 604-611.
  • Handle: RePEc:eee:jetheo:v:154:y:2014:i:c:p:604-611
    DOI: 10.1016/j.jet.2014.10.004
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    References listed on IDEAS

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    1. Nicola Persico, 2000. "Information Acquisition in Auctions," Econometrica, Econometric Society, vol. 68(1), pages 135-148, January.
    2. Bernhard Eckwert & Itzhak Zilcha, 2008. "Efficiency of Screening and Labor Income Inequality," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 77-98, February.
    3. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    4. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    5. Juan-JosÈ Ganuza & JosÈ S. Penalva, 2010. "Signal Orderings Based on Dispersion and the Supply of Private Information in Auctions," Econometrica, Econometric Society, vol. 78(3), pages 1007-1030, May.
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    Citations

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    Cited by:

    1. Leoni, Patrick & Lundtofte, Frederik, 2017. "Information, stochastic dominance and bidding: The case of Treasury auctions," Economics Letters, Elsevier, vol. 153(C), pages 80-82.
    2. Bernhard Eckwert & Itzhak Zilcha, 2018. "The Role of Colleges within the Higher Education Sector," CESifo Working Paper Series 7135, CESifo Group Munich.

    More about this item

    Keywords

    Information; Dispersion orderings; Decision making under uncertainty;

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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