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Aggregate information, common knowledge, and agreeing not to bet


  • Tsakas, Elias

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


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

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    References listed on IDEAS

    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. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
    11. Hanson, Robin, 2002. "Disagreement is unpredictable," Economics Letters, Elsevier, vol. 77(3), pages 365-369, November.
    12. Brandenburger, Adam & Dekel, Eddie, 1987. "Common knowledge with probability 1," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 237-245, June.
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    More about this item


    Gamble; private information; communication; common knowledge;

    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

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