IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v53y2013i1p61-83.html
   My bibliography  Save this article

Evaluations of epistemic components for resolving the muddy children puzzle

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-012-0735-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-012-0735-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Xiao Luo, 2016. "Rational beliefs in rationalizability," Theory and Decision, Springer, vol. 81(2), pages 189-198, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. John Geanakoplos, 1993. "Common Knowledge," Cowles Foundation Discussion Papers 1062, Cowles Foundation for Research in Economics, Yale University.
    2. Spyros Galanis, 2013. "Unawareness of theorems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 41-73, January.
    3. Rodrigues-Neto, José Alvaro, 2009. "From posteriors to priors via cycles," Journal of Economic Theory, Elsevier, vol. 144(2), pages 876-883, March.
    4. Julia Mortera & A. Philip Dawid, 2017. "A Note on Prediction Markets," Departmental Working Papers of Economics - University 'Roma Tre' 0215, Department of Economics - University Roma Tre.
    5. Pivato, Marcus, 2008. "The Discursive Dilemma and Probabilistic Judgement Aggregation," MPRA Paper 8412, University Library of Munich, Germany.
    6. Shyam Sunder, 2001. "Knowing What Others Know: Common Knowledge, Accounting, and Capital Markets," Yale School of Management Working Papers ysm326, Yale School of Management, revised 01 Feb 2002.
    7. Galanis, Spyros, 2013. "Trade and the value of information under unawareness," Discussion Paper Series In Economics And Econometrics 1313, Economics Division, School of Social Sciences, University of Southampton.
    8. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    9. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    10. Mark Fey & Kristopher W. Ramsay, 2006. "The Common Priors Assumption," Journal of Conflict Resolution, Peace Science Society (International), vol. 50(4), pages 607-613, August.
    11. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
    12. Dindo, Pietro & Massari, Filippo, 2020. "The wisdom of the crowd in dynamic economies," Theoretical Economics, Econometric Society, vol. 15(4), November.
    13. Giacomo Bonanno & Klaus Nehring, "undated". "Introduction To The Semantics Of Belief And Common Belief," Department of Economics 97-19, California Davis - Department of Economics.
    14. Timo Ehrig & Jaison Manjaly & Aditya Singh & Shyam Sunder, 2022. "Adaptive Rationality in Strategic Interaction: Do Emotions Regulate Thinking About Others?," Strategy Science, INFORMS, vol. 7(4), pages 330-349, December.
    15. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 11(5), pages 895-953, November.
    16. Michael Suk-Young Chwe, 1998. "Culture, Circles, And Commercials," Rationality and Society, , vol. 10(1), pages 47-75, February.
    17. Roy Chen & Yan Chen & Yohanes E. Riyanto, 2021. "Best practices in replication: a case study of common information in coordination games," Experimental Economics, Springer;Economic Science Association, vol. 24(1), pages 2-30, March.
    18. Moritz Meyer-ter-Vehn & Lones Smith & Katalin Bognar, 2008. "We Can't Argue Forever, But We Should Argue As Long As Possible," 2008 Meeting Papers 1022, Society for Economic Dynamics.
    19. Franck Paolucci, 2007. "Des contraintes aux contributions des investissements en R&D aux Etats-Unis," Documents de Travail de l'OFCE 2007-16, Observatoire Francais des Conjonctures Economiques (OFCE).
    20. Kris De Jaegher, 2015. "Beneficial Long Communication in the Multiplayer Electronic Mail Game," American Economic Journal: Microeconomics, American Economic Association, vol. 7(4), pages 233-251, November.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:53:y:2013:i:1:p:61-83. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.