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Incomplete-Information Models of Large Economies with Anonymity: Existence and Uniqueness of Common Priors

Author

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  • Martin Hellwig

    (Max Planck Institute for Research on Collective Goods, Bonn)

Abstract

The paper provides a speci?cation of belief systems for models of large economies with anonymity in which aggregate states depend only on cross-section distributions of types. For belief systems satisfying certain conditions of mutual absolute continuity, the paper gives a necessary and sufficient condition for the existence of a common prior. Under the given conditions, the common prior is unique.

Suggested Citation

  • Martin Hellwig, 2011. "Incomplete-Information Models of Large Economies with Anonymity: Existence and Uniqueness of Common Priors," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2011_08, Max Planck Institute for Research on Collective Goods.
    • Handle: RePEc:mpg:wpaper:2011_08
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    References listed on IDEAS

    as
    1. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
    2. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    3. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    4. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 1-22, October.
    5. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    6. Martin Hellwig & Felix Bierbrauer, 2009. "Public Good Provision in a Large Economy," 2009 Meeting Papers 1062, Society for Economic Dynamics.
    7. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    8. Sun, Yeneng & Zhang, Yongchao, 2009. "Individual risk and Lebesgue extension without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 432-443, January.
    9. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
    10. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    2. Martin Hellwig, 2015. "Financial Stability and Monetary Policy," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_10, Max Planck Institute for Research on Collective Goods.
    3. Felix Bierbrauer & Martin Hellwig, 2011. "Mechanism Design and Voting for Public-Good Provision," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2011_31, Max Planck Institute for Research on Collective Goods.
    4. Felix J. Bierbrauer & Martin F. Hellwig, 2015. "Public-Good Provision in Large Economies," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_12, Max Planck Institute for Research on Collective Goods.
    5. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.

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    More about this item

    Keywords

    Large Economy; Belief systems; consistency; common prior;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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