IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v95y2000i2p169-185.html
   My bibliography  Save this article

Quantified Beliefs and Believed Quantities

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
    • Handle: RePEc:eee:jetheo:v:95:y:2000:i:2:p:169-185
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022-0531(00)92670-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    2. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 301-314.
    3. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
    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. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    2. Di Tillio, Alfredo & Halpern, Joseph Y. & Samet, Dov, 2014. "Conditional belief types," Games and Economic Behavior, Elsevier, vol. 87(C), pages 253-268.
    3. Satoshi Fukuda, 2024. "On the consistency among prior, posteriors, and information sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 521-565, September.
    4. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.
    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. Samet, Dov, 1999. "Bayesianism without learning," Research in Economics, Elsevier, vol. 53(2), pages 227-242, June.
    7. Hellman, Ziv, 2011. "Iterated expectations, compact spaces, and common priors," Games and Economic Behavior, Elsevier, vol. 72(1), pages 163-171, May.
    8. Samet, Dov, 2022. "The impossibility of agreeing to disagree: An extension of the sure-thing principle," Games and Economic Behavior, Elsevier, vol. 132(C), pages 390-399.
    9. Fukuda, Satoshi, 2020. "Formalizing common belief with no underlying assumption on individual beliefs," Games and Economic Behavior, Elsevier, vol. 121(C), pages 169-189.
    10. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 399-410, May.
    11. , & ,, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
    12. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Dov Samet, 1997. "On the Triviality of High-Order Probabilistic Beliefs," Game Theory and Information 9705001, University Library of Munich, Germany.
    3. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    4. ,, 2008. "Subjective expected utility in games," Theoretical Economics, Econometric Society, vol. 3(3), September.
    5. Weinstein, Jonathan & Yildiz, Muhamet, 2007. "Impact of higher-order uncertainty," Games and Economic Behavior, Elsevier, vol. 60(1), pages 200-212, July.
    6. Satoshi Fukuda, 2024. "On the consistency among prior, posteriors, and information sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 521-565, September.
    7. Dov Samet, 1996. "Looking Backwards, Looking Inwards: Priors and Introspection," Game Theory and Information 9610007, University Library of Munich, Germany.
    8. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    9. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
    10. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    11. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    12. Shmuel Zamir, 2008. "Bayesian games: Games with incomplete information," Discussion Paper Series dp486, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    13. Samet, Dov, 1999. "Bayesianism without learning," Research in Economics, Elsevier, vol. 53(2), pages 227-242, June.
    14. Qin, Cheng-Zhong & Yang, Chun-Lei, 2013. "Finite-order type spaces and applications," Journal of Economic Theory, Elsevier, vol. 148(2), pages 689-719.
    15. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
    16. Fukuda, Satoshi, 2020. "Formalizing common belief with no underlying assumption on individual beliefs," Games and Economic Behavior, Elsevier, vol. 121(C), pages 169-189.
    17. , & , & ,, 2006. "Topologies on types," Theoretical Economics, Econometric Society, vol. 1(3), pages 275-309, September.
    18. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Tsakas, Elias, 2014. "Rational belief hierarchies," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 121-127.
    20. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:95:y:2000:i:2:p:169-185. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.