Most economic analyses presume that there are limited differences in the prior beliefs of individuals, an assumption most often justified by the argument that sufficient common experiences and observations will eliminate disagreements. We investigate this claim using a simple model of Bayesian learning. Two individuals with di.erent priors observe the same infinite sequence of signals about some underlying parameter. Existing results in the liter- ature establish that when individuals know the interpretation of signals, under very mild conditions, there will be asymptotic agreementtheir assessments will eventually agree. In contrast, we look at an environment in which individuals are uncertain about the inter- pretation of signals, meaning that they have non-degenerate probability distributions over the conditional distribution of signals given the underlying parameter. When priors on the parameter and the conditional distribution of signals have full support, we show the following: (1) Individuals will never agree, even after observing the same infinite sequence of signals. (2) Before observing the signals, they believe with probability 1 that their posteri- ors about the underlying parameter will fail to converge. (3) Observing the same (infinite) sequence of signals may lead to a divergence of opinion rather than the typically-presumed convergence. We then characterize the conditions for asymptotic agreement under “approx- imate certainty”–i.e., as we look at the limit where uncertainty about the interpretation of the signals disappears. When the family of probability distributions of signals given the parameter has rapidly-varying tails (such as the normal or the exponential distributions), approximate certainty restores asymptotic agreement. However, when the family of proba- bility distributions has regularly-varying tails (such as the Pareto, the log-normal, and the t-distributions), asymptotic agreement does not obtain even in the limit as the amount of uncertainty disappears. We also discuss how lack of common priors implied by the type of learning in this paper interacts with economic behavior in various different situations, including games of common interest, coordination, asset trading and bargaining.
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Find related papers by JEL classification: C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
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Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)
Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2006.
"Common Learning,"
Cowles Foundation Discussion Papers
1575R, Cowles Foundation, Yale University, revised Jun 2007.
[Downloadable!]
Other versions:
Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2006.
"Common Learning,"
Levine's Bibliography
321307000000000355, UCLA Department of Economics.
[Downloadable!]
Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2007.
"Common Learning,"
PIER Working Paper Archive
07-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
[Downloadable!]
Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2008.
"Common Learning,"
Econometrica,
Econometric Society, vol. 76(4), pages 909-933, 07.
[Downloadable!] (restricted)