IDEAS home Printed from https://ideas.repec.org/p/mpg/wpaper/2011_08.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.coll.mpg.de/pdf_dat/2011_08online.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    2. 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.
    3. 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.
    4. Martin Hellwig & Felix Bierbrauer, 2009. "Public Good Provision in a Large Economy," 2009 Meeting Papers 1062, Society for Economic Dynamics.
    5. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    6. 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.
    7. 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.
    8. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
    9. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    2. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    3. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
    4. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.
    5. José Alvaro Rodrigues-Neto, 2012. "Cycles of length two in monotonic models," ANU Working Papers in Economics and Econometrics 2012-587, Australian National University, College of Business and Economics, School of Economics.
    6. Fiorini, Luciana C. & Rodrigues-Neto, José A., 2017. "Self-consistency, consistency and cycles in non-partitional knowledge models," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 11-21.
    7. Mendolicchio, Concetta & Paolini, Dimitri & Pietra, Tito, 2012. "Investments in education and welfare in a two-sector, random matching economy," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 367-385.
    8. Luciana C. Fiorini & José A. Rodrigues-Neto, 2014. "Self-Consistency and Common Prior in Non-Partitional Knowledge Models," ANU Working Papers in Economics and Econometrics 2014-621, Australian National University, College of Business and Economics, School of Economics.
    9. , & , P. & , & ,, 2015. "Strategic uncertainty and the ex-post Nash property in large games," Theoretical Economics, Econometric Society, vol. 10(1), January.
    10. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    11. José Rodrigues-Neto, 2014. "Monotonic models and cycles," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 403-413, May.
    12. Jonas Hedlund & Carlos Oyarzun, 2018. "Imitation in heterogeneous populations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 937-973, June.
    13. Hellman, Ziv, 2011. "Iterated expectations, compact spaces, and common priors," Games and Economic Behavior, Elsevier, vol. 72(1), pages 163-171, May.
    14. Ziv Hellman & Miklós Pintér, 2022. "Charges and bets: a general characterisation of common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 567-587, November.
    15. 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.
    16. Martin Hellwig, 2010. "Utilitarian mechanism design for an excludable public good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(3), pages 361-397, September.
    17. Sun, Xiang & Sun, Yeneng & Yu, Haomiao, 2020. "The individualistic foundation of equilibrium distribution," Journal of Economic Theory, Elsevier, vol. 189(C).
    18. Martins-da-Rocha, V. Filipe, 2010. "Interim efficiency with MEU-preferences," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1987-2017, September.
    19. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
    20. Chen, Enxian & Qiao, Lei & Sun, Xiang & Sun, Yeneng, 2022. "Robust perfect equilibrium in large games," Journal of Economic Theory, Elsevier, vol. 201(C).

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mpg:wpaper:2011_08. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Marc Martin (email available below). General contact details of provider: https://edirc.repec.org/data/mppggde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.