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Blackwell's informativeness theorem using diagrams

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  • de Oliveira, Henrique

Abstract

This paper gives a simple proof of Blackwell's theorem on the ranking of information structures. The proof extends naturally to environments where information arrives over time (leading to the notion of adapted garbling) and environments where information is diffused among multiple players (leading to the notion of independent garbling).

Suggested Citation

  • de Oliveira, Henrique, 2018. "Blackwell's informativeness theorem using diagrams," Games and Economic Behavior, Elsevier, vol. 109(C), pages 126-131.
    • Handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:126-131
    DOI: 10.1016/j.geb.2017.12.008
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    References listed on IDEAS

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    1. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    2. Leshno, Moshe & Spector, Yishay, 1992. "An elementary proof of Blackwell's theorem," Mathematical Social Sciences, Elsevier, vol. 25(1), pages 95-98, December.
    3. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    4. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    5. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2010. "Signaling and mediation in games with common interests," Games and Economic Behavior, Elsevier, vol. 68(2), pages 670-682, March.
    6. Bielinska-Kwapisz, Agnieszka, 2003. "Sufficiency in Blackwell's theorem," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 21-25, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Khan, M. Ali & Yu, Haomiao & Zhang, Zhixiang, 2024. "On comparisons of information structures with infinite states," Journal of Economic Theory, Elsevier, vol. 218(C).
    2. Dillenberger, David & Krishna, R. Vijay & Sadowski, Philipp, 2023. "Subjective information choice processes," Theoretical Economics, Econometric Society, vol. 18(2), May.
    3. Mark Whitmeyer & Cole Williams, 2024. "Dynamic Signals," Papers 2407.16648, arXiv.org.
    4. Wu, Wenhao, 2023. "A geometric Blackwell’s order," Economics Letters, Elsevier, vol. 226(C).
    5. Alexander M. Jakobsen, 2021. "An Axiomatic Model of Persuasion," Econometrica, Econometric Society, vol. 89(5), pages 2081-2116, September.
    6. Mark Whitmeyer & Cole Williams, 2024. "Comparisons of Sequential Experiments for Additively Separable Problems," Papers 2405.13709, arXiv.org.
    7. Chady Jabbour & Anis Hoayek & Jean-Michel Salles, 2022. "Formalizing a Two-Step Decision-Making Process in Land Use: Evidence from Controlling Forest Clearcutting Using Spatial Information," Land, MDPI, vol. 12(1), pages 1-17, December.
    8. Andrew Kosenko, 2021. "Algebraic Properties of Blackwell's Order and A Cardinal Measure of Informativeness," Papers 2110.11399, arXiv.org.
    9. Li, Jian & Zhou, Junjie, 2020. "Information order in monotone decision problems under uncertainty," Journal of Economic Theory, Elsevier, vol. 187(C).
    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. Henrique de Oliveira & Yuhta Ishii & Xiao Lin, 2021. "Robust Aggregation of Correlated Information," Papers 2106.00088, arXiv.org, revised Sep 2024.

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    More about this item

    Keywords

    Blackwell's theorem; Information; Garbling; Category theory;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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