Discussion Paper 1011, "Social Learning with Local Interactions", by Ianni, A. and Guarino, A.
We study a simple dynamic model of social learning with local informational exter-nalities. 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 among 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, and observe both neighbours, 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), and observe one neighbour, 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.
Keywords: Social Learning, Bayesian Learning, Local Informational External-ities, Path Dependence, Consensus, Clustering, Convergence Rates.