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Quantified Beliefs and Believed Quantities

  • Samet, Dov

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  2. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
  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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