The Dynamics of Social Influence

Individual behaviors such as smoking, fashion, and the adoption of new products is influenced by taking account of others' actions in one's decisions.  We study social influence in a heterogeneous population and analyze the long-run behavior of the dynamics.  We distinguish between cases in which social influence arises from responding to the number of current adopters, and cases in which social influence arises from responding to the cumulative usage.  We identify the equilibria of the dynamics and show which equilibrium is observed in the long-run.  We find that the models exhibit different behaviour and hence this differentiation is of importance.  We also provide an intuition for the different outcomes.