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Looking Backwards, Looking Inwards: Priors and Introspection

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  • Dov Samet

    (Faculty of Management Tel Aviv University)

Abstract

The three notions studied here are Bayesian priors, invariant priors and introspection. A prior for an agent is Bayesian, if it agrees with the agent's posterior beliefs when conditioned on them. A prior is invariant, if it is the average, with respect to itself, of the posterior beliefs. Finally, an agent is introspective, if he is certain of his own beliefs. We show that a prior is Bayesian, if and only if it is invariant, and the agent is almost surely introspective. We show how to edogenize priors, and how to express the events that an agent has a Bayesian or invariant prior. Finally, we study properties of the endogenized common prior.

Suggested Citation

  • Dov Samet, 1996. "Looking Backwards, Looking Inwards: Priors and Introspection," Game Theory and Information 9610007, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:9610007
    Note: Type of Document - Postscript ; prepared on Unix; pages: 13
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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. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    5. Dov Samet, 1996. "Common Priors and Markov Chains," Game Theory and Information 9610008, University Library of Munich, Germany.
    6. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
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    Cited by:

    1. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1997. "Patterns, Types, and Bayesian Learning," Game Theory and Information 9711002, University Library of Munich, Germany.
    2. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.
    3. Dov Samet, 1997. "On the Triviality of High-Order Probabilistic Beliefs," Game Theory and Information 9705001, University Library of Munich, Germany.

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    More about this item

    Keywords

    Bayesian model; prior; common prior; type spaces; introspection;
    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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