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Evaluations of epistemic components for resolving the muddy children puzzle

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  • J. Kline

Abstract

We evaluate the 3 child muddy children puzzle using the epistemic logic of shallow depths $$\text{ GL}_{EF}$$ . This system is used to evaluate what components are necessary for a resolution. These components include the basic beliefs of a child, the necessary depths of the epistemic structures, and the observations about the inactions of others added after a stage. These are all given explicitly, and their necessity is examined. We formulate the concept of a resolution as a process of inferences, actions, observations, and belief changes. We give three theorems. The first one gives a specific resolution, in which no common knowledge is involved. The second theorem states that any resolution has length of at least 3. The third theorem shows that the resolution given in the first theorem is minimal in various senses. In this manner, the necessary components for a resolution of the puzzle are evaluated. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • J. Kline, 2013. "Evaluations of epistemic components for resolving the muddy children puzzle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 61-83, May.
    • Handle: RePEc:spr:joecth:v:53:y:2013:i:1:p:61-83
    DOI: 10.1007/s00199-012-0735-x
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    References listed on IDEAS

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    1. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
    2. Mariko Yasugi & Sobei H. Oda, 2002. "A note on the wise girls puzzle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(1), pages 145-156.
    3. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
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    Cited by:

    1. Xiao Luo, 2016. "Rational beliefs in rationalizability," Theory and Decision, Springer, vol. 81(2), pages 189-198, August.
    2. Mamoru Kaneko, 2013. "Symposium: logic and economics—interactions between subjective thinking and objective worlds," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 1-8, May.

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    More about this item

    Keywords

    Syntactic approach; Shallow depths of epistemic structures; Gentzen-style sequent calculus; Classical and epistemic inferences; D80; D83;
    All these keywords.

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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