In this paper we consider a hierarchical model of spatial electoral competition with two dominant players (incumbents) and one entrant. The incumbents engage in a non-cooperative game against each other and act as Stackelberg leaders with respect to a vote-maximizing entrant. We prove that the equilibrium of this game, called a hierarchical equilibrium, exists and is unique for an arbitrary single-peaked distribution of voters' ideal points. Moreover, we fully characterize the set of equilibrium strategies and show its equivalence to the set of strategies generated by a perfect-foresight equilibrium.