Three-Candidate Spatial Competition When Candidates Have Valence: Asymmetric Voter Density and Plurality Maximization

I study both local and global Nash equilibria of a model of three-candidate unidimensional spatial competition. In the model, candidates may have different non-policy characteristics (valence). Generalizing the base model studied in Evrenk (2009a;b) the model allows for an asymmetric voter density as well as plurality-maximizing candidates. Unlike the standard Hotelling-Downs model of multi-candidate competition, under an asymmetric density with (heterogenous) vote-maximizing candidates a pure strategy Nash equilibrium (PSNE) exists. Further, this PSNE is free from several non-plausible features of PSNE under a symmetric density. When candidates are plurality-maximizers, some of the PSNE are supported by paradoxical candidate behavior. Further, when voter density is asymmetric and candidates are plurality-maximizers, there are several non-monotonicities in the PSNE.