Social Reinforcement: Cascades, Entrapment, and Tipping

The actions of di¤erent agents sometimes reinforce each other. Examples are network e¤ects and the threshold models used by sociologists as well as Leibenstein’s “bandwagon e¤ects.”We model such situations as a game with increasing di¤erences, 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 ine¢ cient equilibria can be tipped to the e¢ cient one, a result of interest in the context of coordination problems. We characterize the smallest tipping set. Key words tipping, security, increasing di¤erences, cascading, interdependence, networks, entrapment, thresholds. JEL classi…cation: C 72, D 80, H 23, The choices made by di¤erent individuals can reinforce each other. Network externalities provide an obvious example. Explanations for Microsoft’s domination of the operating system market, eBay’s domination of the online auction market, and the permanence of the QWERTY keyboard layout have been based on network e¤ects.1 The rapid growth in popularity of social networking sites such as Facebook and MySpace also illustrates the importance of social reinforcement: people join because their friends have already done so. In his theory of entrapment, Avinash Dixit [10] exploits reinforcing e¤ects of people’s choices to show how some may be entrapped into joining a club in spite of the fact that its existence makes them worse o¤.2 There is an early precedent for the importance of social reinforcement in Heal is at Columbia Business School, [email protected]. Kunreuther is at the Wharton School of the University of Pennsylvania, [email protected]. We are especially grateful to Larry Samuelson for assistance with this paper, and also grateful to Doug Bernheim, Vince Crawford, Rachel Croson, Avinash Dixit, Charley Holt, Alan Kirman, Robert Porter and a referee for constructive comments. See Carl Shapiro and Hal Varian [28], Brian Arthur [1]. For reviews of this area see Charles Manski [23] and Nicholas Economides [12] The popularity of the QWERTY keyboard may be an illustration of entrapment, in the sense that a redesigned keyboard would enable everyone to type much faster than they currently do; however, there is no incentive for any one individual to learn the new system on his own because the keyboard he needs to purchase will have to be specially made and hence relatively expensive. Furthermore it may not be available in other locations in which he is required to type.