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How common are common priors?

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  • Hellman, Ziv
  • Samet, Dov

Abstract

To answer the question in the title we vary agentsʼ beliefs against the background of a fixed knowledge space, that is, a state space with a partition for each agent. Beliefs are the posterior probabilities of agents, which we call type profiles. We then ask what is the topological size of the set of consistent type profiles, those that are derived from a common prior (or a common improper prior in the case of an infinite state space). The answer depends on what we term the tightness of the partition profile. A partition profile is tight if in some state it is common knowledge that any increase of any single agentʼs knowledge results in an increase in common knowledge. We show that for partition profiles that are tight the set of consistent type profiles is topologically large, while for partition profiles that are not tight this set is topologically small.

Suggested Citation

  • Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    • Handle: RePEc:eee:gamebe:v:74:y:2012:i:2:p:517-525
    DOI: 10.1016/j.geb.2011.08.008
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    1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
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    5. Yaw Nyarko, 2010. "Most games violate the common priors doctrine," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 189-194, March.
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    Cited by:

    1. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.
    2. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    3. Collevecchio, Andrea & LiCalzi, Marco, 2012. "The probability of nontrivial common knowledge," Games and Economic Behavior, Elsevier, vol. 76(2), pages 556-570.
    4. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    5. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
    6. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    7. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 399-410, May.
    8. Christian W. Bach & Andrés Perea, 2023. "Structure‐preserving transformations of epistemic models," Economic Inquiry, Western Economic Association International, vol. 61(3), pages 693-719, July.
    9. Halpern, Joseph Y. & Kets, Willemien, 2015. "Ambiguous language and common priors," Games and Economic Behavior, Elsevier, vol. 90(C), pages 171-180.
    10. 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.
    11. Yaw Nyarko, 2010. "Most games violate the common priors doctrine," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 189-194, March.
    12. Hellman, Ziv, 2013. "Weakly rational expectations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 496-500.
    13. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).

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    More about this item

    Keywords

    Common prior; Common knowledge; Knowledge; Belief;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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