Social Reinforcement: Cascades, Entrapment and Tipping

There are many social situations in which the actions of different agents reinforce each other. These include network effects and the threshold models used by sociologists (Granovetter, Watts) as well as Leibenstein's "bandwagon effects." We model such situations as a game with increasing differences, and show that tipping of equilibria as discussed by Schelling, cascading and Dixit's results on clubs with entrapment are natural consequences of this mutual reinforcement. If there are several equilibria, one of which Pareto dominates, then we show that the inefficient equilibria can be tipped to the efficient one, a result of interest in the context of coordination problems.