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Quantified beliefs and believed quantities

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Author Info

  • Dov Samet

    (Faculty of Management Tel Aviv University)

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

Paper provided by EconWPA in its series Game Theory and Information with number 9805003.

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Length: 13 pages
Date of creation: 10 May 1998
Date of revision:
Handle: RePEc:wpa:wuwpga:9805003

Note: Type of Document - pdflatex, postscript; prepared on windows 95; pages: 13
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Web page: http://128.118.178.162

Related research

Keywords: Harsanyi type spaces; estimation; probabilistic beliefs; ergodic theory;

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References

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  1. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, vol. 28(3), pages 301-314.
  2. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
  3. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
  4. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  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. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer, vol. 42(2), pages 399-410, May.
  2. 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.
  3. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.
  4. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
  5. Ehud Lehrer & Dov Samet, 2003. "Agreeing to agree," Game Theory and Information 0310005, EconWPA.
  6. Hellman, Ziv, 2007. "Iterated Expectations, Compact Spaces and Common Priors," MPRA Paper 3794, University Library of Munich, Germany.
  7. Dov Samet, 1999. "Bayesianism without Learning," Game Theory and Information 9902004, EconWPA.

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