In an interdependent world the risks faced by any one agent depend not only on its choices but also on those of all others. Expectations about others' choices will influence investments in risk management and the outcome can be suboptimal for everyone. We model this as the Nash equilibrium of a game and give conditions for such a suboptimal equilibrium to be tipped to an optimal one. We also characterize the smallest coalition to tip an equilibrium, the minimum critical coalition, and show that this is also the cheapest critical coalition, so that there is no less expensive way to move the system from the suboptimal to the optimal equilibrium. We illustrate these results by reference to airline security and the control of infectious diseases via vaccination.