Robust Intervention in Networks

In economic settings such as learning, social behavior, and financial contagion, agents interact through interdependent networks. This paper examines how a decision maker (DM) can design an optimal intervention strategy under network uncertainty, modeled as a zero-sum game against an adversarial ``Nature'' that reconfigures the network within an uncertainty set. Using duality, we characterize the DM's unique robust intervention and identify the worst-case network structure, which exhibits a rank-1 property, concentrating risk along the intervention strategy. We analyze the costs of robustness, distinguishing between global and local uncertainty, and examine the role of higher-order uncertainties in shaping intervention outcomes. Our findings highlight key trade-offs between maximizing influence and mitigating uncertainty, offering insights into robust decision-making. This framework has applications in policy design, economic regulation, and strategic interventions in dynamic networks, ensuring their resilience against uncertainty in network structures.