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Agreeing To Disagree: A Survey

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  • Klaus Nehring
  • Giacomo Bonanno

    (Department of Economics, University of California Davis)

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

  • Klaus Nehring & Giacomo Bonanno, 2003. "Agreeing To Disagree: A Survey," Working Papers 9718, University of California, Davis, Department of Economics.
  • Handle: RePEc:cda:wpaper:97-18
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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. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
    5. Tarbush, Bassel, 2016. "Counterfactuals in “agreeing to disagree” type results," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 125-133.
    6. Boot, Arnoud W A & Thakor, Anjan, 2003. "The Economic Value of Flexibility When There is Disagreement," CEPR Discussion Papers 3709, C.E.P.R. Discussion Papers.
    7. Bach, Christian W. & Perea, Andrés, 2013. "Agreeing to disagree with lexicographic prior beliefs," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 129-133.
    8. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.

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