IDEAS home Printed from https://ideas.repec.org/p/hhs/gunwpe/0254.html
   My bibliography  Save this paper

Aggregate information, common knowledge, and agreeing not to bet

Author

Listed:
  • Tsakas, Elias

    (Department of Economics, School of Business, Economics and Law, Göteborg University)

Abstract

I consider a gamble where the sum of the distributed payoffs is proportionate to the number of participants. I show that no subset of the population can agree to participate in the bet, if the size of the group is commonly known. Repeated announcements of the number of the participants leads the population to agree not to bet.

Suggested Citation

  • Tsakas, Elias, 2007. "Aggregate information, common knowledge, and agreeing not to bet," Working Papers in Economics 254, University of Gothenburg, Department of Economics.
    • Handle: RePEc:hhs:gunwpe:0254
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/2077/4575
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
    2. Nielsen, Lars Tyge, 1984. "Common knowledge, communication, and convergence of beliefs," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 1-14, August.
    3. Robin Hanson, 1998. "Consensus By Identifying Extremists," Theory and Decision, Springer, vol. 44(3), pages 293-301, June.
    4. Milgrom, Paul, 1981. "An Axiomatic Characterization of Common Knowledge," Econometrica, Econometric Society, vol. 49(1), pages 219-222, January.
    5. Nielsen, Lars Tyge, 1995. "Common Knowledge of a Multivariate Aggregate Statistic," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(1), pages 207-216, February.
    6. McKelvey, Richard D & Page, Talbot, 1986. "Common Knowledge, Consensus, and Aggregate Information," Econometrica, Econometric Society, vol. 54(1), pages 109-127, January.
    7. Rubinstein, Ariel & Wolinsky, Asher, 1990. "On the logic of "agreeing to disagree" type results," Journal of Economic Theory, Elsevier, vol. 51(1), pages 184-193, June.
    8. Nielsen, Lars Tyge, et al, 1990. "Common Knowledge of an Aggregate of Expectations," Econometrica, Econometric Society, vol. 58(5), pages 1235-1239, September.
    9. Cave, Jonathan A. K., 1983. "Learning to agree," Economics Letters, Elsevier, vol. 12(2), pages 147-152.
    10. 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.
    11. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
    12. Hanson, Robin, 2002. "Disagreement is unpredictable," Economics Letters, Elsevier, vol. 77(3), pages 365-369, November.
    13. Brandenburger, Adam & Dekel, Eddie, 1987. "Common knowledge with probability 1," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 237-245, June.
    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. Tsakas, Elias & Voorneveld, Mark, 2007. "Efficient communication, common knowledge, and consensus," Working Papers in Economics 255, University of Gothenburg, Department of Economics.
    2. Giacomo Bonanno & Klaus Nehring, "undated". "Agreeing To Disagree: A Survey," Department of Economics 97-18, California Davis - Department of Economics.
    3. John Geanakoplos, 1993. "Common Knowledge," Cowles Foundation Discussion Papers 1062, Cowles Foundation for Research in Economics, Yale University.
    4. Bernard Walliser, 1991. "Logique épistémique et théorie des jeux," Revue Économique, Programme National Persée, vol. 42(5), pages 801-832.
    5. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
    6. Bonanno, G. & Nehring, K., 1995. "Intersubjective Consistency of Beliefs and the Logic of Common Belief," Department of Economics 95-08, California Davis - Department of Economics.
    7. Lucie Ménager, 2004. "A note on consensus and common knowledge of an aggregate of decisions," Cahiers de la Maison des Sciences Economiques v04006, Université Panthéon-Sorbonne (Paris 1).
    8. 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.
    9. Ménager, Lucie, 2008. "Consensus and common knowledge of an aggregate of decisions," Games and Economic Behavior, Elsevier, vol. 62(2), pages 722-731, March.
    10. 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.
    11. Fukuda, Satoshi, 2019. "Epistemic foundations for set-algebraic representations of knowledge," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 73-82.
    12. 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.
    13. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.
    14. , & ,, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.
    15. Galanis, S. & Ioannou, C. & Kotronis, S., 2019. "Information Aggregation Under Ambiguity: Theory and Experimental Evidence," Working Papers 20/05, Department of Economics, City University London.
    16. 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.
    17. Nielsen, Lars Tyge, 1996. "Common knowledge: The case of linear regression," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 285-304.
    18. Robin Hanson, 2003. "For Bayesian Wannabes, Are Disagreements Not About Information?," Theory and Decision, Springer, vol. 54(2), pages 105-123, March.
    19. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    20. Hanson, Robin, 2002. "Disagreement is unpredictable," Economics Letters, Elsevier, vol. 77(3), pages 365-369, November.

    More about this item

    Keywords

    Gamble; private information; communication; common knowledge;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hhs:gunwpe:0254. 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: Ann-Christin Räätäri Nyström (email available below). General contact details of provider: https://edirc.repec.org/data/naiguse.html .

    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.