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The Value of Information - An Axiomatic Approach

Author

Listed:
  • Itzhak Gilboa

    (Northwestern University [Evanston])

  • Ehud Lehrer

    (Northwestern University [Evanston])

Abstract

The following question is addressed: Given a real-valued function on the partitions of a measure space, what are necessary and sufficient conditions in order that it be the value of information function for a Bayesian decision maker? A characterization is provided, and the analysis reveals a close relationship to cooperative game theory. The tools developed for characterization can also be used to derive somewhat surprising results regarding the properties of information functions.

Suggested Citation

  • Itzhak Gilboa & Ehud Lehrer, 1991. "The Value of Information - An Axiomatic Approach," Post-Print hal-00753232, HAL.
    • Handle: RePEc:hal:journl:hal-00753232
    DOI: 10.1016/0304-4068(91)90002-B
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    References listed on IDEAS

    as
    1. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    2. Chateauneuf, Alain, 1985. "On the existence of a probability measure compatible with a total preorder on a Boolean algebra," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 43-52, February.
    3. Hirshleifer, J & Riley, John G, 1979. "The Analytics of Uncertainty and Information-An Expository Survey," Journal of Economic Literature, American Economic Association, vol. 17(4), pages 1375-1421, December.
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    Citations

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    Cited by:

    1. Lehrer, Ehud, 2005. "Updating non-additive probabilities-- a geometric approach," Games and Economic Behavior, Elsevier, vol. 50(1), pages 42-57, January.
    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. Lefort, Jean-Philippe, 2009. "Guessing the beliefs," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 846-853, December.
    4. Ehud Lehrer & Dinah Rosenberg, 2003. "Information and Its Value in Zero-Sum Repeated Games," Game Theory and Information 0312003, University Library of Munich, Germany.
    5. Azrieli, Yaron & Lehrer, Ehud, 2008. "The value of a stochastic information structure," Games and Economic Behavior, Elsevier, vol. 63(2), pages 679-693, July.
    6. Aouani, Zaier & Chateauneuf, Alain, 2008. "Exact capacities and star-shaped distorted probabilities," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 185-194, September.
    7. Costis Skiadas, 1991. "Conditioning and Aggregation of Preferences," Discussion Papers 1010, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    9. Lorenzo Bastianello & Alain Chateauneuf & Bernard Cornet, 2022. "Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules," Papers 2203.16292, arXiv.org.
    10. Borgonovo, Emanuele & Hazen, Gordon B. & Jose, Victor Richmond R. & Plischke, Elmar, 2021. "Probabilistic sensitivity measures as information value," European Journal of Operational Research, Elsevier, vol. 289(2), pages 595-610.
    11. Michel de Lara & Olivier Gossner, 2020. "Payoffs-Beliefs Duality and the Value of Information," Post-Print hal-01941006, HAL.
    12. Ehud Lehrer & Tao Wang, 2022. "The Value of Information in Stopping Problems," Papers 2205.06583, arXiv.org.
    13. Gilboa, Itzhak & Lehrer, Ehud, 1991. "Global Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 129-147.
    14. Bernard de Meyer & Ehud Lehrer & Dinah Rosenberg, 2009. "Evaluating information in zero-sum games with incomplete information on both sides," Post-Print halshs-00390625, HAL.
    15. Lehrer, Ehud & Rosenberg, Dinah, 2006. "What restrictions do Bayesian games impose on the value of information?," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 343-357, June.
    16. Gordon Hazen & Emanuele Borgonovo & Xuefei Lu, 2023. "Information Density in Decision Analysis," Decision Analysis, INFORMS, vol. 20(2), pages 89-108, June.
    17. Rébillé, Yann, 2011. "A Radon-Nikodym approach to measure information," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 170-177, May.
    18. Giovanni Rossi, 2003. "Global Coalitional Games," Department of Economics University of Siena 415, Department of Economics, University of Siena.
    19. Jean-Philippe Lefort, 2006. "Comparison of experts in the non-additive case," Post-Print halshs-00130451, HAL.
    20. 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.
    21. Alexander M. Jakobsen, 2021. "An Axiomatic Model of Persuasion," Econometrica, Econometric Society, vol. 89(5), pages 2081-2116, September.
    22. Eran Shmaya, 2006. "The Value of Information Structures in Zero-sum Games with Lack of Information on One Side," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 155-165, August.
    23. Bernard De Meyer & Ehud Lehrer & Dinah Rosenberg, 2010. "Evaluating Information in Zero-Sum Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 851-863, November.

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