Common Learning

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 that when each agent's signal space is finite, the agents will commonly learn its value, i.e., that the true value of the parameter will become approximate common-knowledge. 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.

Keywords: Common learning, Common belief, Private signals, Private beliefs

JEL Classification: D82, D83

Suggested Citation: Suggested Citation

Cripps, Martin and Cripps, Martin and Ely, Jeffrey C. and Mailath, George J. and Samuelson, Larry, Common Learning (June 20, 2007). Cowles Foundation Discussion Paper No. 1575R, PIER Working Paper No. 07-018, Available at SSRN: https://ssrn.com/abstract=995818

Martin Cripps

Washington University in St. Louis - John M. Olin Business School ( email )

One Brookings Drive
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University College London - Department of Economics ( email )

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Jeffrey C. Ely

Northwestern University - Department of Economics ( email )

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Evanston, IL 60208
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George J. Mailath (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
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Philadelphia, PA 19104-6297
United States
215-898-7908 (Phone)
215-573-2057 (Fax)

HOME PAGE: http://web.sas.upenn.edu/gmailath/