IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v132y2022icp390-399.html
   My bibliography  Save this article

The impossibility of agreeing to disagree: An extension of the sure-thing principle

Author

Listed:
  • Samet, Dov

Abstract

The impossibility of agreeing to disagree in the non-probabilistic setup means that agents cannot commonly know their decisions unless they are all the same. We study the relation of this property to the sure thing principle when it is expressed in epistemic terms. We show that it can be presented in two equivalent ways: one is in terms of knowledge operators, which we call the principle of follow the knowledgeable, the other is in terms of kens—bodies of agents' knowledge—which we call independence of irrelevant knowledge. The latter can be easily extended to a property which is equivalent to the impossibility of agreeing to disagree.

Suggested Citation

  • Samet, Dov, 2022. "The impossibility of agreeing to disagree: An extension of the sure-thing principle," Games and Economic Behavior, Elsevier, vol. 132(C), pages 390-399.
    • Handle: RePEc:eee:gamebe:v:132:y:2022:i:c:p:390-399
    DOI: 10.1016/j.geb.2022.01.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825622000227
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2022.01.016?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. Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
    2. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
    3. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    4. Cave, Jonathan A. K., 1983. "Learning to agree," Economics Letters, Elsevier, vol. 12(2), pages 147-152.
    5. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
    Full references (including those not matched with items on IDEAS)

    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. Tarbush, Bassel, 2011. "Agreeing to disagree with generalised decision functions," MPRA Paper 29066, University Library of Munich, Germany.
    3. Tarbush, Bassel, 2016. "Counterfactuals in “agreeing to disagree” type results," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 125-133.
    4. , & ,, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
    5. Gossner, Olivier & Tsakas, Elias, 2007. "Testing Rationality on Primitive Knowledge," Working Papers in Economics 275, University of Gothenburg, Department of Economics.
    6. Shyam NMI Sunder, 2001. "Knowing What Others Know: Common Knowledge, Accounting, and Capital Markets," Yale School of Management Working Papers ysm213, Yale School of Management.
    7. Ariel Rubinstein & Asher Wolinsky, 1988. "A Comment on the Logic of 'Agreeing to Disagree' Type Results," Discussion Papers 822, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    9. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.
    10. Tsakas, Elias & Voorneveld, Mark, 2007. "Efficient communication, common knowledge, and consensus," Working Papers in Economics 255, University of Gothenburg, Department of Economics.
    11. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    12. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
    13. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
    14. Tsakas, Elias, 2007. "Aggregate information, common knowledge, and agreeing not to bet," Working Papers in Economics 254, University of Gothenburg, Department of Economics.
    15. Luo, Xiao & Ma, Chenghu, 2003. ""Agreeing to disagree" type results: a decision-theoretic approach," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 849-861, November.
    16. Tarbush, Bassel, 2011. "Generalisation of Samet's (2010) agreement theorem," MPRA Paper 29067, University Library of Munich, Germany.
    17. Houy, Nicolas & Ménager, Lucie, 2008. "Communication, consensus and order. Who wants to speak first?," Journal of Economic Theory, Elsevier, vol. 143(1), pages 140-152, November.
    18. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    19. Lucie Ménager, 2005. "Consensus, Communication and Knowledge: an Extension with Bayesian Agents," Cahiers de la Maison des Sciences Economiques v05031, Université Panthéon-Sorbonne (Paris 1), revised Jan 2006.
    20. Bonanno, Giacomo & Nehring, Klaus, 1998. "On the logic and role of Negative Introspection of Common Belief," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 17-36, January.

    More about this item

    Keywords

    Sure thing principle; Agreeing to disagree; Common knowledge;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:eee:gamebe:v:132:y:2022:i:c:p:390-399. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.