  We study the incentives that agents have to invest in costly protection
against cascading failures in networked systems. Applications include
vaccination, computer security and airport security. Agents are connected
through a network and can fail either intrinsically or as a result of the
failure of a subset of their neighbors. We characterize the equilibrium based
on an agent's failure probability and derive conditions under which equilibrium
strategies are monotone in degree (i.e. in how connected an agent is on the
network). We show that different kinds of applications (e.g. vaccination,
malware, airport/EU security) lead to very different equilibrium patterns of
investments in protection, with important welfare and risk implications. Our
equilibrium concept is flexible enough to allow for comparative statics in
terms of network properties and we show that it is also robust to the
introduction of global externalities (e.g. price feedback, congestion).
