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From posteriors to priors via cycles

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  • Rodrigues-Neto, José Alvaro

Abstract

We present new necessary and sufficient conditions for checking if a set of players' posteriors may come from a common prior. A simple diagrammatic device calculates the join and meet of players' knowledge partitions. Each cycle in the diagram has a corresponding cycle equation. Posteriors are consistent with a common prior if and only if all cycle equations are satisfied. We prove that in games of two players, where the join partition has only singletons, a common prior exists if each player's distribution of beliefs over the elements of her opponent's partition is independent of her own private information.

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  • Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
    • Handle: RePEc:eee:jetheo:v:144:y:2009:i:2:p:876-883
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    References listed on IDEAS

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    Cited by:

    1. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    2. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    3. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.
    4. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
    5. José A. Rodrigues‐Neto, 2015. "Monotonic Knowledge Models, Cycles, Linear Versions and Auctions with Differential, Finite Information," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 25-37, June.
    6. 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.
    7. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    8. 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.
    9. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    10. José Rodrigues-Neto, 2014. "Monotonic models and cycles," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 403-413, May.
    11. 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.
    12. 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.

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