Naive Learning with Uninformed Agents

38 Pages Posted: 4 Feb 2019 Last revised: 5 Feb 2019

See all articles by Abhijit V. Banerjee

Abhijit V. Banerjee

Massachusetts Institute of Technology (MIT) - Department of Economics

Emily Breza

Harvard University

Arun G. Chandrasekhar

Stanford University - Department of Economics

Markus M. Mobius

Microsoft Corporation - Microsoft Research New England; University of Michigan at Ann Arbor - School of Information; National Bureau of Economic Research (NBER)

Date Written: January 2019

Abstract

The DeGroot model has emerged as a credible alternative to the standard Bayesian model for studying learning on networks, offering a natural way to model naive learning in a complex setting. One unattractive aspect of this model is the assumption that the process starts with every node in the network having a signal. We study a natural extension of the DeGroot model that can deal with sparse initial signals. We show that an agent's social influence in this generalized DeGroot model is essentially proportional to the number of uninformed nodes who will hear about an event for the first time via this agent. This characterization result then allows us to relate network geometry to information aggregation. We identify an example of a network structure where essentially only the signal of a single agent is aggregated, which helps us pinpoint a condition on the network structure necessary for almost full aggregation. We then simulate the modeled learning process on a set of real world networks; for these networks there is on average 21.6% information loss. We also explore how correlation in the location of seeds can exacerbate aggregation failure. Simulations with real world network data show that with clustered seeding, information loss climbs to 35%.

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Suggested Citation

Banerjee, Abhijit V. and Breza, Emily and Chandrasekhar, Arun G. and Mobius, Markus M., Naive Learning with Uninformed Agents (January 2019). NBER Working Paper No. w25497. Available at SSRN: https://ssrn.com/abstract=3328320

Abhijit V. Banerjee (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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Emily Breza

Harvard University ( email )

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Arun G. Chandrasekhar

Stanford University - Department of Economics ( email )

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Markus M. Mobius

Microsoft Corporation - Microsoft Research New England ( email )

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University of Michigan at Ann Arbor - School of Information ( email )

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HOME PAGE: http://www.markusmobius.org

National Bureau of Economic Research (NBER) ( email )

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HOME PAGE: http://www.markusmobius.org

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