Abstract
This note considers gambles that take place even if only some—but not all—individuals agree to participate. I show that the bet cannot take place if it is commonly known how many individuals are willing to participate.
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References
Aumann RJ (1976) Agreeing to disagree. Ann Stat 4: 1236–1239
Geanakoplos J, Polemarchakis H (1982) We can’t disagree forever. J Econ Theory 28: 192–200
Hanson R (1998) Consensus by identifying extremists. Theory Decis 44: 293–301
Hanson R (2002) Disagreement is unpredictable. Econ Lett 77: 365–369
Milgrom P, Stokey N (1980) Information, trade, and common knowledge. J Econ Theory 26: 17–27
Nielsen LT (1995) Common knowledge of a multivariate aggregate statistic. Int Econ Rev 36: 207–216
Nielsen LT, Brandenburger A, Geanakoplos J, McKelvey R, Page T (1990) Common knowledge of an aggregate of expectations. Econometrica 58: 1235–1239
Sebenius J, Geanakoplos J (1983) Don’t bet on it: contingent agreements with asymmetric information. J Am Stat Assoc 78: 424–426
Acknowledgements
I am indebted to Alpaslan Akay, Geir Asheim, Martin Dufwenberg, Amanda Friedenberg, John Geanakoplos, Andrés Perea, Jeff Steif, Mark Voorneveld, Jörgen Weibull, an anonymous referee and an associate editor for valuable comments and fruitful discussions. I would also like to thank the University of California, Berkeley and the Stockholm School of Economics for their hospitality while working on this project. The financial support from the Adlerbertska Research Foundation is gratefully acknowledged.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Tsakas, E. Aggregate information, common knowledge and agreeing not to bet. Int J Game Theory 40, 111–117 (2011). https://doi.org/10.1007/s00182-010-0226-x
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DOI: https://doi.org/10.1007/s00182-010-0226-x