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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.

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Paper provided by California Davis - Department of Economics in its series Department of Economics with number 97-18.

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Handle: RePEc:fth:caldec:97-18

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Cited by:
  1. Dov Samet, 2006. "Agreeing to disagree: The non-probabilistic case," Levine's Bibliography 321307000000000536, UCLA Department of Economics.
  2. Arnoud W.A. Boot & Anjan V. Thakor, 2003. "The Economic Value of Flexibility when there is Disagreement," Tinbergen Institute Discussion Papers 03-002/2, Tinbergen Institute.
  3. Bach, Christian W. & Perea, Andrés, 2013. "Agreeing to disagree with lexicographic prior beliefs," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 129-133.
  4. Arnoud W.A. Boot & Anjan V. Thakor, 2003. "The Economic Value of Flexibility when there is Disagreement," Tinbergen Institute Discussion Papers 03-002/2, Tinbergen Institute.
  5. Robin Hanson, 2003. "For Bayesian Wannabes, Are Disagreements Not About Information?," Theory and Decision, Springer, vol. 54(2), pages 105-123, March.

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