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The value of information - An axiomatic approach

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  • Gilboa, Itzhak
  • Lehrer, Ehud

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.
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Suggested Citation

  • Gilboa, Itzhak & Lehrer, Ehud, 1991. "The value of information - An axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 443-459.
    • Handle: RePEc:eee:mateco:v:20:y:1991:i:5:p:443-459
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    References listed on IDEAS

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    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. Costis Skiadas, 1991. "Conditioning and Aggregation of Preferences," Discussion Papers 1010, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. 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.
    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. Michel de Lara & Olivier Gossner, 2020. "Payoffs-Beliefs Duality and the Value of Information," Post-Print hal-01941006, HAL.
    7. Gilboa, Itzhak & Lehrer, Ehud, 1991. "Global Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 129-147.
    8. Jean-Philippe Lefort, 2006. "Comparison of experts in the non-additive case," Post-Print halshs-00130451, HAL.
    9. 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.
    10. 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.
    11. Kops, Christopher & Pasichnichenko, Illia, 2023. "Testing negative value of information and ambiguity aversion," Journal of Economic Theory, Elsevier, vol. 213(C).
    12. Lefort, Jean-Philippe, 2009. "Guessing the beliefs," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 846-853, December.
    13. Ehud Lehrer & Dinah Rosenberg, 2003. "Information and Its Value in Zero-Sum Repeated Games," Game Theory and Information 0312003, University Library of Munich, Germany.
    14. Aouani, Zaier & Chateauneuf, Alain, 2008. "Exact capacities and star-shaped distorted probabilities," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 185-194, September.
    15. 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.
    16. Lorenzo Bastianello & Alain Chateauneuf & Bernard Cornet, 2022. "Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules," Papers 2203.16292, arXiv.org.
    17. Ehud Lehrer & Tao Wang, 2022. "The Value of Information in Stopping Problems," Papers 2205.06583, arXiv.org.
    18. 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.
    19. Rommeswinkel, Hendrik & Chang, Hung-Chi & Hsu, Wen-Tai, 2023. "Preference for Knowledge," Journal of Economic Theory, Elsevier, vol. 214(C).
    20. Gordon Hazen & Emanuele Borgonovo & Xuefei Lu, 2023. "Information Density in Decision Analysis," Decision Analysis, INFORMS, vol. 20(2), pages 89-108, June.
    21. Rébillé, Yann, 2011. "A Radon-Nikodym approach to measure information," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 170-177, May.
    22. Giovanni Rossi, 2003. "Global Coalitional Games," Department of Economics University of Siena 415, Department of Economics, University of Siena.
    23. 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.
    24. Alexander M. Jakobsen, 2021. "An Axiomatic Model of Persuasion," Econometrica, Econometric Society, vol. 89(5), pages 2081-2116, September.
    25. 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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