Controlling Complex Contagions

Abstract: Many social and economic behaviors—from the adoption of new technologies or cultural norms, to protest participation—require social reinforcement to spread. That is, agents take an action if and only if enough of their neighbors in a network do so too. These phenomena are called complex contagions. However, deriving comparatives statics in model of these behaviors has proven elusive, which has rendered policy recommendations for network design intractable. We introduce a new approach by analyzing complex contagions on random graphs. This approach unlocks powerful comparative statics that allow for precise policy recommendations. We find that equilibrium behavior jumps discontinuously from zero at a critical cut-off in network connectivity, and exhibits diminishing returns thereafter. Optimal network design reveals a “missing middle” in the designer’s optimal choice: network connectivity is either set at the critical cut-off or substantially above it. Finally, we discuss a number of interventions that a principal can use to control complex contagions.