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Quantified Beliefs and Believed Quantities

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  • Samet, Dov

Abstract

That people estimate quantities, or have beliefs about them, is a daily observable phenomenon. People also quantify their beliefs, at least in theory, by ascribing to them probability numbers. It is shown that quantified beliefs and estimations give rise to the same model, that of a type space, and can therefore be viewed as the two sides of the same coin. We study the axiom that an agent's estimation of his own estimation is correct, showing it to be weaker than the introspection axiom, according to which an agent is certain of his own probabilistic beliefs. It implies, however, that the agent is certain that he is introspective, and it is equivalent to the axioms of averaging and conditioning, which are expressed in terms of probabilistic beliefs.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 95 (2000)
Issue (Month): 2 (December)
Pages: 169-185

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Handle: RePEc:eee:jetheo:v:95:y:2000:i:2:p:169-185

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
  2. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  3. Harsanyi, John C., 1994. "Games with Incomplete Information," Nobel Prize in Economics documents 1994-1, Nobel Prize Committee.
  4. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, vol. 28(3), pages 301-314.
  5. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
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Cited by:
  1. Lehrer, Ehud & Samet, Dov, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
  2. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer, vol. 42(2), pages 399-410, May.
  3. A. Heifetz & Ph. Mongin, 1998. "Probability logic for type spaces," THEMA Working Papers 98-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  4. Hellman, Ziv, 2007. "Iterated Expectations, Compact Spaces and Common Priors," MPRA Paper 3794, University Library of Munich, Germany.
  5. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
  6. Dov Samet, 1999. "Bayesianism without Learning," Game Theory and Information 9902004, EconWPA.
  7. Pierpaolo Battigalli & Alfredo Di Tillio & Dov Samet, 2011. "Strategies and interactive beliefs in dynamic games," Working Papers 375, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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