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On the Triviality of High-Order Probabilistic Beliefs

Author

Listed:
  • Dov Samet

    (Faculty of Management Tel-Aviv University)

Abstract

Several axioms concerning probabilistic beliefs are examined here, and the relations between them are established, using belief spaces that generalize Harsanyi type spaces. Two axioms concerning high-order probabilistic beliefs are investigated in particular. The first is the triviality axiom, which says that one is certain (that is, has a belief of degree one) of one's own beliefs. The second is the averaging axiom, which states that a first order belief concerning some fact F is the average of all degrees of beliefs concerning F, weighted by the degrees given to them by the second order beliefs. It is shown that one whose beliefs satisfy the averaging axiom must be certain that his beliefs satisfy the triviality axiom.

Suggested Citation

  • Dov Samet, 1997. "On the Triviality of High-Order Probabilistic Beliefs," Game Theory and Information 9705001, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:9705001
    Note: Type of Document - Postscript/Acrobat; prepared on Windows 95; to print on ; pages: 20
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    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. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
    3. 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).
    4. Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
    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.
    7. Dov Samet, 1996. "Looking Backwards, Looking Inwards: Priors and Introspection," Game Theory and Information 9610007, University Library of Munich, Germany.
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    Cited by:

    1. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
    2. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.

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    JEL classification:

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

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