Collapse of Social Engagement and its Prevention by Local Recruitments
Social networks sometimes collapse. The threshold model of collective actions has been widely adopted as a theoretical paradigm to understand this phenomenon, but previous investigations focused on the irreversible K-core pruning process starting from random initial activity patterns. Here we study the vulnerability and resilience of social engagement as a network alliance problem, and find that equilibrium alliance configurations (but not the out-of-equilibrium ones obtained from irreversible pruning) may experience two distinct dynamical transitions as the number of active nodes gradually shrinks. In the intermediate phase bounded by the weak and strong tipping points, an equilibrium alliance is highly vulnerable to single-node-triggered cascading failures, yet all these global collapse events can be successfully suppressed by a simple least-effort local recruitment mechanism which flips a few flippable inactive nodes.