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Information Validates the Prior: A Theorem on Bayesian Updating and Applications

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  • Navin Kartik
  • Frances Lee
  • Wing Suen

Abstract

We develop a result on expected posteriors for Bayesians with heterogenous priors, dubbed information validates the prior (IVP). Under familiar ordering requirements, Anne expects a (Blackwell) more informative experiment to bring Bob's posterior mean closer to Anne's prior mean. We apply the result in two contexts of games of asymmetric information: voluntary testing or certification, and costly signaling or falsification. IVP can be used to determine how an agent's behavior responds to additional exogenous or endogenous information. We discuss economic implications.

Suggested Citation

  • Navin Kartik & Frances Lee & Wing Suen, 2020. "Information Validates the Prior: A Theorem on Bayesian Updating and Applications," Papers 2005.05714, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:2005.05714
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    References listed on IDEAS

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    1. Alonso, Ricardo & Câmara, Odilon, 2016. "Bayesian persuasion with heterogeneous priors," Journal of Economic Theory, Elsevier, vol. 165(C), pages 672-706.
    2. Kreps, David M. & Francetich, Alejandro, 2014. "Bayesian Inference Does Not Lead You Astray . . . On Average," Research Papers 3059, Stanford University, Graduate School of Business.
    3. Weiss, Andrew, 1983. "A Sorting-cum-Learning Model of Education," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 420-442, June.
    4. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
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    Cited by:

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    2. Onuchic, Paula & Ray, Debraj, 2023. "Conveying value via categories," Theoretical Economics, Econometric Society, vol. 18(4), November.
    3. Chang, Dongkyu & Vong, Allen, 2021. "Perverse Ethical Concerns: Online Platforms and Offline Conflicts," MPRA Paper 110507, University Library of Munich, Germany.
    4. Giampaolo Bonomi, 2023. "The Disagreement Dividend," Papers 2308.06607, arXiv.org, revised Jan 2024.

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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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