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The value of a stochastic information structure

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  • Azrieli, Yaron
  • Lehrer, Ehud

Abstract

Upon observing a signal, a Bayesian decision maker updates her probability distribution over the state space, chooses an action, and receives a payoff that depends on the state and the action taken. An information structure determines the set of possible signals and the probability of each signal given a state. For a fixed decision problem, the value of an information structure is the maximal expected utility that the decision maker can get when the observed signals are governed by this structure. Thus, every decision problem induces a preference order over information structures according to their value. We characterize preference orders that can be obtained in this way. We also characterize the functions defined over information structures that measure their value.

Suggested Citation

  • Azrieli, Yaron & Lehrer, Ehud, 2008. "The value of a stochastic information structure," Games and Economic Behavior, Elsevier, vol. 63(2), pages 679-693, July.
    • Handle: RePEc:eee:gamebe:v:63:y:2008:i:2:p:679-693
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    References listed on IDEAS

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    1. Gilboa, Itzhak & Lehrer, Ehud, 1991. "The value of information - An axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 443-459.
    2. Eliaz, Kfir & Spiegler, Ran, 2006. "Can anticipatory feelings explain anomalous choices of information sources?," Games and Economic Behavior, Elsevier, vol. 56(1), pages 87-104, July.
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    Citations

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    Cited by:

    1. 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.
    2. Mark Whitmeyer, 2022. "Making Information More Valuable," Papers 2210.04418, arXiv.org, revised Dec 2023.
    3. 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.
    4. Ludvig Sinander, 2023. "Optimism, overconfidence, and moral hazard," Papers 2304.08343, arXiv.org, revised Mar 2024.
    5. Ambuehl, Sandro & Li, Shengwu, 2018. "Belief updating and the demand for information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 21-39.
    6. Alexander M. Jakobsen, 2021. "An Axiomatic Model of Persuasion," Econometrica, Econometric Society, vol. 89(5), pages 2081-2116, September.
    7. Michel de Lara & Olivier Gossner, 2020. "Payoffs-Beliefs Duality and the Value of Information," Post-Print hal-01941006, HAL.
    8. Bernard Herskovic & João Ramos, 2020. "Acquiring Information through Peers," American Economic Review, American Economic Association, vol. 110(7), pages 2128-2152, July.
    9. 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.
    10. 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.
    11. Ehud Lehrer & Tao Wang, 2022. "The Value of Information in Stopping Problems," Papers 2205.06583, arXiv.org.
    12. 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.
    13. Li, Jian & Zhou, Junjie, 2016. "Blackwell's informativeness ranking with uncertainty-averse preferences," Games and Economic Behavior, Elsevier, vol. 96(C), pages 18-29.
    14. 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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    More about this item

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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