Learning in society

In the canonical learning model, the multi-armed bandit with independent arms, a decision maker learns about the different alternatives by his experience only. It is well known that an optimal experimentation strategy for this problem sometimes leads the best alternative to be dropped altogether, the so-called Rothschild effect. Many situations of interest, however, involve learning from individual experience and the experience of others. This paper shows that learn-ing in society can overcome the Rothschild effect. We consider an economy with a continuum of infinitely lived agents where each one of them faces a two-armed bandit and the unknown stochastic payoffs of each arm are the same for all agents. In each period, agents are randomly and anonymously matched in pairs, where they observe their partners ’ current action choice. We establish that if initial beliefs are sufficiently heterogeneous, then the fraction of agents who choose the superior arm converges to one in any perfect bayesian equilibrium of this game