Social Reinforcement: Cascades, Entrapment, and Tipping

The actions of different agents sometimes reinforce each other. Examples are network effects and the threshold models used by sociologists as well as (Harvey) Leibenstein's "bandwagon effects." We model such situations as a game with increasing differences, and show that tipping of equilibria, cascading, and clubs with entrapment are natural consequences of this mutual reinforcement. If there are several equilibria, one of which Pareto dominates, then the inefficient equilibria can be tipped to the efficient one, a result of interest in the context of coordination problems. We characterize the smallest tipping set.