The Hotelling–Downs model with runoff voting

We consider the Hotelling–Downs model with n⩾3n⩾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 locate at distinct positions), though only divergent equilibria are robust to free entry. Moreover, two-policy equilibria exist under any distribution of votersʼ ideal policies, while equilibria with more than two policies exist generically but under restrictive conditions that we characterize.