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A tight sufficient condition for Radner-Stiglitz nonconcavity in the value of information

Author

Listed:
  • Michel de Lara

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTech)

  • L. Gilotte

    (CIRED - centre international de recherche sur l'environnement et le développement - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - EHESS - École des hautes études en sciences sociales - AgroParisTech - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper deals with the existence of a nonconcavity in the value of information, as was first explained by Radner and Stiglitz [A nonconcavity in the value of information, in: M. Boyer, R.E. Kihlstrom (Eds.), Bayesian Models in Economic Theory, Elsevier Science Publishers, Amsterdam, 1984, pp. 33-52 (Chapter 3)]. After defining infinitesimal information distance variationIIDV, we find that IIDV = 0 is sufficient for a zero marginal value of information at the null. This is a condition only on the information structure and in particular is independent of the decision maker's preferences. This condition is tight: when IIDV > 0, there exists a payoff function for which the marginal value of information at the null is positive under general assumptions. © 2007.

Suggested Citation

  • Michel de Lara & L. Gilotte, 2007. "A tight sufficient condition for Radner-Stiglitz nonconcavity in the value of information," Post-Print hal-00716396, HAL.
    • Handle: RePEc:hal:journl:hal-00716396
    DOI: 10.1016/j.jet.2007.01.014
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    Citations

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    Cited by:

    1. Michel de Lara & Olivier Gossner, 2020. "Payoffs-Beliefs Duality and the Value of Information," Post-Print hal-01941006, HAL.
    2. Mark Whitmeyer, 2022. "Making Information More Valuable," Papers 2210.04418, arXiv.org, revised Dec 2023.
    3. Mark Whitmeyer, 2024. "Call the Dentist! A (Con-)Cavity in the Value of Information," Papers 2404.01190, arXiv.org.
    4. Mark Whitmeyer, 2024. "Can One Hear the Shape of a Decision Problem?," Papers 2403.06344, arXiv.org, revised Apr 2024.
    5. van Staden, Heletjé E. & Boute, Robert N., 2021. "The effect of multi-sensor data on condition-based maintenance policies," European Journal of Operational Research, Elsevier, vol. 290(2), pages 585-600.
    6. Peter I. Frazier & Warren B. Powell, 2010. "Paradoxes in Learning and the Marginal Value of Information," Decision Analysis, INFORMS, vol. 7(4), pages 378-403, December.
    7. Michel De Lara & Olivier Gossner, 2017. "An instrumental approach to the value of information," Working Papers 2017-49, Center for Research in Economics and Statistics.

    More about this item

    Keywords

    Value of information;

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