Aggregate information, common knowledge, and agreeing not to bet
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.
|Date of creation:||18 Jun 2007|
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- McKelvey, Richard D & Page, Talbot, 1986. "Common Knowledge, Consensus, and Aggregate Information," Econometrica, Econometric Society, vol. 54(1), pages 109-127, January.
- Hanson, Robin, 2002. "Disagreement is unpredictable," Economics Letters, Elsevier, vol. 77(3), pages 365-369, November.
- Paul Milgrom, 1979.
"An Axiomatic Characterization of Common Knowledge,"
393R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Nielsen, Lars Tyge, et al, 1990. "Common Knowledge of an Aggregate of Expectations," Econometrica, Econometric Society, vol. 58(5), pages 1235-1239, September.
- 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.
- Lars Tyge Nielsen, 1990. "Common Knowledge of a Multivariate Aggregate Statistic," CEPR Financial Markets Paper 0003, European Science Foundation Network in Financial Markets, c/o C.E.P.R, 77 Bastwick Street, London EC1V 3PZ..
- Robin Hanson, 1998. "Consensus By Identifying Extremists," Theory and Decision, Springer, vol. 44(3), pages 293-301, June.
- D. Samet, 1987.
"Ignoring Ignorance and Agreeing to Disagree,"
749, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982.
"We can't disagree forever,"
Journal of Economic Theory,
Elsevier, vol. 28(1), pages 192-200, October.
- Nielsen, Lars Tyge, 1984. "Common knowledge, communication, and convergence of beliefs," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 1-14, August.
- Cave, Jonathan A. K., 1983. "Learning to agree," Economics Letters, Elsevier, vol. 12(2), pages 147-152.
- 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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