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How Common Are Common Priors?

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  • Ziv Hellman
  • Dov Samet

Abstract

To answer the question in the title we vary agents' 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 agent's knowledge results in an increase in common knowledge. We show that for partition profiles which are tight the set of consistent type profiles is topologically large, while for partition profiles which are not tight this set is topologically small.

Suggested Citation

  • Ziv Hellman & Dov Samet, 2010. "How Common Are Common Priors?," Discussion Paper Series dp532, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp532
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    References listed on IDEAS

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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.
    2. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Robert J. Aumann, 1998. "Common Priors: A Reply to Gul," Econometrica, Econometric Society, vol. 66(4), pages 929-938, July.
    4. Nyarko, Yaw, 1991. "Most Games Violate the Harsanyi Doctrine," Working Papers 91-39, C.V. Starr Center for Applied Economics, New York University.
    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.
    6. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    7. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
    8. Faruk Gul, 1998. "A Comment on Aumann's Bayesian View," Econometrica, Econometric Society, vol. 66(4), pages 923-928, July.
    9. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
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    Cited by:

    1. Halpern, Joseph Y. & Kets, Willemien, 2015. "Ambiguous language and common priors," Games and Economic Behavior, Elsevier, vol. 90(C), pages 171-180.
    2. Hellwig, Martin F., 2013. "From posteriors to priors via cycles: An addendum," Economics Letters, Elsevier, vol. 118(3), pages 455-458.
    3. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    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. Collevecchio, Andrea & LiCalzi, Marco, 2012. "The probability of nontrivial common knowledge," Games and Economic Behavior, Elsevier, vol. 76(2), pages 556-570.
    6. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
    7. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 399-410, May.
    8. 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.
    9. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    10. 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.
    11. Hellman, Ziv, 2013. "Weakly rational expectations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 496-500.
    12. 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.

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    More about this item

    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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