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Universally Rational Belief Hierarchies

Author

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  • ELIAS TSAKAS

    (Department of Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

Abstract

In a recent paper, Tsakas [2013Rational belief hierarchies, Journal of Mathematical Economics, Maastricht University] introduced the notion of rational beliefs. These are Borel probability measures that assign a rational probability to every Borel event. Then, he constructed the corresponding Harsanyi type space model that represents the rational belief hierarchies. As he showed, there are rational types that are associated with a non-rational probability measure over the product of the underlying space of uncertainty and the opponent's types. In this paper, we define the universally rational belief hierarchies, as those that do not exhibit this property. Then, we characterize them in terms of a natural restriction imposed directly on the belief hierarchies.

Suggested Citation

  • Elias Tsakas, 2014. "Universally Rational Belief Hierarchies," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-12.
    • Handle: RePEc:wsi:igtrxx:v:16:y:2014:i:01:n:s0219198914400039
    DOI: 10.1142/S0219198914400039
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    References listed on IDEAS

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    1. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part B : The Central Results," LIDAM Discussion Papers CORE 1994021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396, October.
    3. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," LIDAM Discussion Papers CORE 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915, October.
    5. MERTENS, Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part C : Further Developments," LIDAM Discussion Papers CORE 1994022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Michael Greinecker & Christopher Kah, 2021. "Pairwise Stable Matching in Large Economies," Econometrica, Econometric Society, vol. 89(6), pages 2929-2974, November.

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    More about this item

    Keywords

    Epistemic game theory; rational numbers; belief hierarchies; type spaces; C72; D83;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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