Quantified beliefs and believed quantities
AbstractThat 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by EconWPA in its series Game Theory and Information with number 9805003.
Length: 13 pages
Date of creation: 10 May 1998
Date of revision:
Note: Type of Document - pdflatex, postscript; prepared on windows 95; pages: 13
Contact details of provider:
Web page: http://220.127.116.11
Harsanyi type spaces; estimation; probabilistic beliefs; ergodic theory;
Other versions of this item:
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
- D8 - Microeconomics - - Information, Knowledge, and Uncertainty
This paper has been announced in the following NEP Reports:
- NEP-ALL-1998-10-02 (All new papers)
- NEP-GTH-1998-10-02 (Game Theory)
- NEP-MIC-1998-10-02 (Microeconomics)
- NEP-TID-1998-10-02 (Technology & Industrial Dynamics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Heifetz, Aviad & Samet, Dov, 1998.
"Topology-Free Typology of Beliefs,"
Journal of Economic Theory,
Elsevier, vol. 82(2), pages 324-341, October.
- Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
- Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, vol. 28(3), pages 301-314.
- Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
- Harsanyi, John C, 1995.
"Games with Incomplete Information,"
American Economic Review,
American Economic Association, vol. 85(3), pages 291-303, June.
- Hellman, Ziv, 2007.
"Iterated Expectations, Compact Spaces and Common Priors,"
3794, University Library of Munich, Germany.
- Hellman, Ziv, 2011. "Iterated expectations, compact spaces, and common priors," Games and Economic Behavior, Elsevier, vol. 72(1), pages 163-171, May.
- Ziv Hellman, 2009. "Iterated Expectations, Compact Spaces, and Common Priors," Discussion Paper Series dp522, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Samet, Dov, 1999.
"Bayesianism without learning,"
Research in Economics,
Elsevier, vol. 53(2), pages 227-242, June.
- Ziv Hellman, 2013.
"Almost common priors,"
International Journal of Game Theory,
Springer, vol. 42(2), pages 399-410, May.
- Heifetz, Aviad & Mongin, Philippe, 2001.
"Probability Logic for Type Spaces,"
Games and Economic Behavior,
Elsevier, vol. 35(1-2), pages 31-53, April.
- Heifetz, A. & Mongin, P., 1998. "Probability Logic for Type Spaces," Papers 9825, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
- 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.
- Lehrer, Ehud & Samet, Dov, 2011.
"Agreeing to agree,"
Econometric Society, vol. 6(2), May.
- 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.
- Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).
If references are entirely missing, you can add them using this form.