Supermodularity and Tipping

We model tipping as a game-theoretic phenomenon and investigate the connection between supermodular games, tipping of equilibria and cascading, and apply the results to issues that arise in the context of homeland security and computer security. We show that tipping and cascading can occur in supermodular games and that "increasing differences" is a sufficient condition for tipping. Supermodularity and tipping of equilibria are closely related. We relate our results to Schelling's early work on tipping.