Network attrition: Theory and policy implications

Networks frequently experience attrition as individual members exit over time. Such departures can significantly impact the behavior of their peers and have cascading effects on overall network activity. We investigate such effects within the framework of the canonical linear-quadratic model of peer influence. We introduce an exogenous shock that removes certain agents from the network, with the key feature that only their immediate neighbors observe these departures. In this setting of incomplete information, we characterize the equilibrium behavior using the Bonacich centrality defined over the belief structures of the agents. We propose the concept of an agent’s expected marginal contribution, quantifying the impact of their presence or absence on aggregate network activity. This metric has direct policy relevance: it enables a planner to identify strategically important agents for targeted intervention: either to preserve their participation and enhance collective effort, or to remove them to reduce activity.