Infrastructure networks are a key feature of an economy. Their functionality depends on the connectivity and sizes of different components and they face a variety of threats, from natural disasters to intelligent attacks. How should networks be defended and designed to ensure the best functionality?

We consider the Hotelling–Downs model with n⩾3 office-seeking candidates and runoff voting. We show that Nash equilibria in pure strategies always exist and that there are typically multiple equilibria, both convergent (all candidates are located at the median) and divergent (candidates...