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Common learning

Cripps, M.W.; Ely, J.; Mailath, G.; Samuelson, L.; (2008) Common learning. Econometrica , 76 (4) pp. 909-933. Green open access

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Abstract

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.

Type: Article
Title: Common learning
Open access status: An open access version is available from UCL Discovery
Publisher version: http://www.econometricsociety.org/abstract.asp?ref...
Language: English
Additional information: The copyright to this article is held by the Econometric Society, http://www.econometricsociety.org. It may be downloaded, printed and reproduced only for personal or classroom use. Absolutely no downloading or copying may be done for, or on behalf of, any for-profit commercial firm or other commercial purpose without the explicit permission of the Econometric Society. For this purpose, contact Claire Sashi, General Manager, at sashi@econometricsociety.org
UCL classification: UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of SandHS > Dept of Economics
URI: http://discovery.ucl.ac.uk/id/eprint/16379
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