Secure and Efficient Networks

More connected networks are often regarded as more efficient, yet increased connectivity can elevate security risks, suggesting that sparser networks may be preferable from a security perspective. In this article, we study the trade-off between efficiency and security in networks. We develop a model in which a Defender and an Attacker engage in a two-stage game. First, the Defender builds a network by establishing costly links, where each node’s value is determined by its degree. Then, the Defender protects a limited number of nodes while the Attacker selects a node to target. Our analysis yields three main insights. First, by choosing the network’s degree sequence in the first stage, the Defender shapes the second-stage equilibrium and limits the expected loss from an attack. Second, the optimal network becomes sparser as link costs rise: a complete network is optimal when costs are low, while the centrally protected star, often regarded as the most secure configuration, arises only when costs are high. Third, when defensive resources are limited, a novel “maxi-core” structure arises in equilibrium, with a fully connected core surrounded by a sparse periphery.