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A note on the wise girls puzzle

Author

Listed:
  • Mariko Yasugi

    (Faculty of Science, Kyoto Sangyo University, Kita-ku, Kyoto 603-8555, JAPAN)

  • Sobei H. Oda

    (Faculty of Economics, Kyoto Sangyo University, Kita-ku, Kyoto 603-8555, JAPAN)

Abstract

This article analyzes the two wise girls puzzle, which is a simpler variant of the so-called three wise men puzzle, with some proof-theoretic tools. We formulate the puzzle in an epistemic logic. Our chief assumption is that the reasoning ability of each player of the puzzle is equivalent to what is described by the epistemic logic. We will interpret the behaviors of the players in the puzzle in terms of unprovability of certain statements. The proof-theoretic tools we employ are consequences of a meta-theorem, known as the cut elimination theorem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:19:y:2002:i:1:p:145-156
    Note: Received: August 1, 2000; revised version: May 15, 2001
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    Citations

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    Cited by:

    1. 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.

    More about this item

    Keywords

    Puzzle; Propositional calculus; Belief operator; Proof-theory; Cut elimination; Unprovability.;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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