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Quantified beliefs and believed quantities

Author

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  • 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.

Suggested Citation

  • Dov Samet, 1998. "Quantified beliefs and believed quantities," Game Theory and Information 9805003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:9805003
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    References listed on IDEAS

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    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. 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).
    5. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    6. 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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    Citations

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    Cited by:

    1. Di Tillio, Alfredo & Halpern, Joseph Y. & Samet, Dov, 2014. "Conditional belief types," Games and Economic Behavior, Elsevier, vol. 87(C), pages 253-268.
    2. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.
    3. Samet, Dov, 1999. "Bayesianism without learning," Research in Economics, Elsevier, vol. 53(2), pages 227-242, June.
    4. Hellman, Ziv, 2011. "Iterated expectations, compact spaces, and common priors," Games and Economic Behavior, Elsevier, vol. 72(1), pages 163-171, May.
    5. , & ,, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
    6. 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.
    7. Ziv Hellman, 2013. "Almost common priors," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 399-410, May.
    8. Heifetz, Aviad, 2006. "The positive foundation of the common prior assumption," Games and Economic Behavior, Elsevier, vol. 56(1), pages 105-120, July.
    9. 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.
    10. Fukuda, Satoshi, 2020. "Formalizing common belief with no underlying assumption on individual beliefs," Games and Economic Behavior, Elsevier, vol. 121(C), pages 169-189.

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    More about this item

    Keywords

    Harsanyi type spaces; estimation; probabilistic beliefs; ergodic theory;
    All these keywords.

    JEL classification:

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

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