Econometrica: Mar 2018, Volume 86, Issue 2
A Theory of Non-Bayesian Social Learning
Pooya Molavi, Alireza Tahbaz‐Salehi, Ali Jadbabaie
This paper studies the behavioral foundations of non‐Bayesian models of learning over social networks and develops a taxonomy of conditions for information aggregation in a general framework. As our main behavioral assumption, we postulate that agents follow social learning rules that satisfy “imperfect recall,” according to which they treat the current beliefs of their neighbors as sufficient statistics for the entire history of their observations. We augment this assumption with various restrictions on how agents process the information provided by their neighbors and obtain representation theorems for the corresponding learning rules (including the canonical model of DeGroot). We then obtain general long‐run learning results that are not tied to the learning rules' specific functional forms, thus identifying the fundamental forces that lead to learning, non‐learning, and mislearning in social networks. Our results illustrate that, in the presence of imperfect recall, long‐run aggregation of information is closely linked to (i) the rate at which agents discount their neighbors' information over time, (ii) the curvature of agents' social learning rules, and (iii) whether their initial tendencies are amplified or moderated as a result of social interactions.
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Supplement to "A Theory of Non-Bayesian Social Learning"
This online supplement contains three parts. Appendix B contains several proofs omitted from the main body of the paper. Appendix C extends the concept of unanimity introduced in Deﬁnition 1 and provides a generalization to Theorem 4 in the paper. Appendix D illustrates that if signals are normally distributed and agents’ prior beliefs are normal, Bayesian updating takes a log-linear form regardless of the structure of the underlying social network.