Social Learning and the Shadow of the Past

In various environments new agents may base their decisions on observations of actions taken by a few other agents in the past. In this paper we analyze a broad class of such social learning processes, and study under what circumstances the initial behavior of the population has a lasting effect. Our main result shows that a population converges to the same behavior independently of the initial state, provided that the expected number of actions observed by each agent is less than one. Moreover, in any environment in which the expected number of observed actions is more than one, there is a learning rule for which the initial state has a lasting impact on future behavior.