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Agreeing to agree

Author

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  • ,

    (School of Mathematical Sciences, Tel Aviv University)

  • ,

    (Faculty of Management, Tel Aviv University)

Abstract

Aumann has shown that agents who have a common prior cannot have common knowledge of their posteriors for event $E$ if these posteriors do not coincide. But given an event $E$, can the agents have posteriors with a common prior such that it is common knowledge that the posteriors for $E$ \emph{do} coincide? We show that a necessary and sufficient condition for this is the existence of a nonempty \emph{finite} event $F$ with the following two properties. First, it is common knowledge at $F$ that the agents cannot tell whether or not $E$ occurred. Second, this still holds true at $F$, when $F$ itself becomes common knowledge.

Suggested Citation

  • , & ,, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
    • Handle: RePEc:the:publsh:578
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    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20110269/5201/186
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    Cited by:

    1. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
    2. Ziv Hellman, 2014. "Countable spaces and common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 193-213, February.
    3. Fukuda, Satoshi, 2021. "Unawareness without AU Introspection," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    4. , & ,, 2017. "Bayesian games with a continuum of states," Theoretical Economics, Econometric Society, vol. 12(3), September.
    5. Fukuda, Satoshi, 2024. "On the axiomatization of an unawareness structure from knowing-whether operators," Journal of Mathematical Economics, Elsevier, vol. 115(C).
    6. Ziv Hellman & Yehuda John Levy, 2022. "Equilibria Existence in Bayesian Games: Climbing the Countable Borel Equivalence Relation Hierarchy," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 367-383, February.
    7. Chen, Yi-Chun & Lehrer, Ehud & Li, Jiangtao & Samet, Dov & Shmaya, Eran, 2015. "Agreeing to agree and Dutch books," Games and Economic Behavior, Elsevier, vol. 93(C), pages 108-116.
    8. Xiong, Siyang, 2012. "Agreeing to agree with uncountable information structures," Games and Economic Behavior, Elsevier, vol. 74(1), pages 442-446.
    9. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
    10. Satoshi Fukuda, 2018. "Representing Unawareness on State Spaces," Working Papers 635, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    11. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.

    More about this item

    Keywords

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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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