  Networks are beneficial to those being connected but can also be used as
carriers of contagious hostile attacks. These attacks are often facilitated by
exploiting corrupt network users. To protect against the attacks, users can
resort to costly defense. The decentralized nature of such protection is known
to be inefficient but the inefficiencies can be mitigated by a careful network
design. Is network design still effective when not all users can be trusted? We
propose a model of network design and defense with byzantine nodes to address
this question. We study the optimal defended networks in the case of
centralized defense and, for the case of decentralized defense, we show that
the inefficiencies due to decentralization can be fully mitigated, despite the
presence of the byzantine nodes.
