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Social and Behavioral Sciences Commons™
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Full-Text Articles in Social and Behavioral Sciences
Common Learning, Martin W. Cripps, Jeffrey C. Ely, George J. Mailath, Larry Samuelson
Common Learning, Martin W. Cripps, Jeffrey C. Ely, George J. Mailath, Larry Samuelson
Cowles Foundation Discussion Papers
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 agents. Does it follow that the agents will commonly learn its value, i.e., that the true value of the parameter will become (approximate) common-knowledge? We show that the answer is affirmative when each agent’s signal space is finite and show by example that common learning can fail when observations come from a countably infinite signal space.
Common Learning, Martin W. Cripps, Jeffrey C. Ely, George J. Mailath, Larry Samuelson
Common Learning, Martin W. Cripps, Jeffrey C. Ely, George J. Mailath, Larry Samuelson
Cowles Foundation Discussion Papers
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.