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Agreeing To Disagree: A Survey

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  • Giacomo Bonanno
  • Klaus Nehring

Abstract

Aumann (1976) put forward a formal definition of common knowledge and used it to prove that two "like minded" individuals cannot "agree to disagree" in the following sense. If they start from a common prior and update the probability of an event E (using Bayes' rule) on the basis of private information, then it cannot be common knowledge between them that individual 1 assigns probability p to E and individual 2 assigns probability q to E with p ¹ q. In other words, if their posteriors of event E are common knowledge then they must coincide. Aumann's Agreement Theorem has given rise to a large literature which we review in this paper. The results are classified according to whether they are probabilistic (Bayesian) or qualitative. Particular attention is paid to the issue of how to interpret the notion of Harsanyi consistency as a (local) property of belief hierarchies.

Suggested Citation

  • Giacomo Bonanno & Klaus Nehring, "undated". "Agreeing To Disagree: A Survey," Department of Economics 97-18, California Davis - Department of Economics.
    • Handle: RePEc:fth:caldec:97-18
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    File URL: http://www.econ.ucdavis.edu/working_papers/97-18.pdf
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    Cited by:

    1. Robin Hanson, 2003. "For Bayesian Wannabes, Are Disagreements Not About Information?," Theory and Decision, Springer, vol. 54(2), pages 105-123, March.
    2. Hoff, Karla & Stiglitz, Joseph E., 2016. "Striving for balance in economics: Towards a theory of the social determination of behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 126(PB), pages 25-57.
    3. Jean Baccelli, 2015. "Do Bets Reveal Beliefs?," Post-Print hal-01462293, HAL.
    4. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    5. Tarbush, Bassel, 2016. "Counterfactuals in “agreeing to disagree” type results," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 125-133.
    6. Pavel Ilinov & Andrei Matveenko & Maxim Senkov & Egor Starkov, 2022. "Optimally Biased Expertise," Papers 2209.13689, arXiv.org, revised Jul 2025.
    7. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
    8. Thakor, Anjan & Boot, Arnoud, 2003. "The Economic Value of Flexibility When There is Disagreement," CEPR Discussion Papers 3709, C.E.P.R. Discussion Papers.
    9. Bach, Christian W. & Perea, Andrés, 2013. "Agreeing to disagree with lexicographic prior beliefs," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 129-133.
    10. Tsakas Elias, 2018. "Agreeing to Disagree with Conditional Probability Systems," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(2), pages 1-7, July.
    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.
    12. Crescenzi, Michele, 2022. "Learning to agree over large state spaces," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    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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