  Social networks of engagement sometimes dramatically collapse. A widely
adopted paradigm to understand this catastrophe dynamics is the threshold model
but previous work only considered the irreversible K-core pruning process and
the resulting kinetic activity patterns. Here we study the network alliance
problem as a simplified model of social engagement by equilibrium statistical
mechanics. Our theory reveals that the surviving kinetic alliances are
out-of-equilibrium and atypical configurations which may become highly
vulnerable to single-node-triggered cascading failures as they relax towards
equilibrium. Our theory predicts that if the fraction of active nodes is beyond
a certain critical value, the equilibrium (typical) alliance configurations
could be protected from cascading failures by a simple least-effort local
intervention strategy. We confirm these results by extensive Monte Carlo
simulations.
