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Econometrica Vol. 76 No. 4 2008

Common Learning

Martin W. Cripps1; Jeffrey C. Ely2; George J. Mailath3,4; Larry Samuelson5,6

1 University College London · 2 Northwestern University · 3 University of the Sciences · 4 Philadelphia University · 5 National Council for Science and the Environment · 6 Yale University

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.

DOI
10.1111/j.1468-0262.2008.00862.x
Volume
76
Issue
4
Pages
909-933
Language
en
Sources
bibtex:phds-export.bib openalex crossref

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