Social learning with local informational externalities

Abstract

We study a simple dynamic model of social learning with local informational externalities. There is a large population of agents, who repeatedly have to choose one, out of two, reversible actions, each of which is optimal in one, out of two, unknown states of the world. Each agent chooses rationally, on the basis of private information (s)he receives by a symmetric binary signal on the state, as well as the observation of the action chosen by their nearest neighbours. Actions can be updated at revision opportunities that agents receive in a random sequential order. Strategies are stationary, in that they do not depend on time, nor on location.
We show that:
if agents receive equally informative signals, then the social learning process is not adequate and the process of actions converges exponentially fast to a configuration where some agents are permanently wrong;
if agents are unequally informed, in that their signal is either fully informative or fully uninformative (both with positive probability), then the social learning process is adequate and everybody will eventually choose the action that is correct given the state. Convergence, however, obtains very slowly, namely at rate √t .
We relate the findings with the literature on social learning and discuss the property of efficiency of the information transmission mechanism under local interaction.

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ORCID for Antonella Ianni: orcid.org/0000-0002-5003-4482

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