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An instrumental approach to the value of information

Author

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  • Michel De Lara

    (CERMICS, ENPC; Université Paris Est)

  • Olivier Gossner

    (CREST; Ecole Polytechnique; London School of Economics)

Abstract

We consider an agent who acquires information on a state of nature from an information structure before facing a decision problem. How much information is worth depends jointly on the decision problem and on the information structure. We represent the decision problem by the set of possible payoffs indexed by states of nature. We establish and exploit the duality between this set on one hand and the value of information function, which maps beliefs to expected payoffs under optimal actions at these beliefs, on the other. We then derive global estimates of the value of information of any information structure from local properties of the value function and of the set of optimal actions taken at the prior belief only.

Suggested Citation

  • 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.
    • Handle: RePEc:crs:wpaper:2017-49
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    References listed on IDEAS

    as
    1. Godfrey Keller & Sven Rady, 1999. "Optimal Experimentation in a Changing Environment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 475-507.
    2. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2013. "Entropy and the Value of Information for Investors," American Economic Review, American Economic Association, vol. 103(1), pages 360-377, February.
    3. Godfrey Keller & Sven Rady & Martin Cripps, 2005. "Strategic Experimentation with Exponential Bandits," Econometrica, Econometric Society, vol. 73(1), pages 39-68, January.
    4. Dirk Bergemann & Juuso Valimaki, 1997. "Market Diffusion with Two-Sided Learning," RAND Journal of Economics, The RAND Corporation, vol. 28(4), pages 773-795, Winter.
    5. Gilboa, Itzhak & Lehrer, Ehud, 1991. "The value of information - An axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 443-459.
    6. Cabrales, Antonio & Gossner, Olivier & Serrano, Roberto, 2017. "A normalized value for information purchases," Journal of Economic Theory, Elsevier, vol. 170(C), pages 266-288.
    7. Azrieli, Yaron & Lehrer, Ehud, 2008. "The value of a stochastic information structure," Games and Economic Behavior, Elsevier, vol. 63(2), pages 679-693, July.
    8. De Lara, Michel & Gilotte, Laurent, 2007. "A tight sufficient condition for Radner-Stiglitz nonconcavity in the value of information," Journal of Economic Theory, Elsevier, vol. 137(1), pages 696-708, November.
    9. repec:hal:pseose:hal-00812682 is not listed on IDEAS
    10. Nicola Persico, 2000. "Information Acquisition in Auctions," Econometrica, Econometric Society, vol. 68(1), pages 135-148, January.
    11. Michel de Lara & L. Gilotte, 2007. "A tight sufficient condition for Radner-Stiglitz nonconcavity in the value of information," Post-Print hal-00716396, HAL.
    12. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
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    Cited by:

    1. Gossner, Olivier & Steiner, Jakub, 2018. "On the cost of misperception: General results and behavioral applications," Journal of Economic Theory, Elsevier, vol. 177(C), pages 816-847.
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    3. Ehud Lehrer & Tao Wang, 2022. "The Value of Information in Stopping Problems," Papers 2205.06583, arXiv.org.

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