Three-candidate competition when candidates have valence: the base case

We study the Nash Equilibrium of three-candidate unidimensional spatial competition when candidates differ in their non-policy characteristics (valence). If the voters’ policy preferences are represented by a strictly convex loss function, and if the voter density is unimodal and symmetric, then a unique, modulo symmetry, Local Nash Equilibrium exists under fairly plausible conditions. The global Nash Equilibrium, however, exists when only one candidate has a valence advantage (or disadvantage) while the other two candidates have the same valence.