Valence politics and equilibrium in spatial election models

Spatial models of two-party or two-candidate competition almost never have pure-strategy Nash equilibria when the issue space has more than one dimension. This paper shows that the introduction of valence issues can create conditions where equilibria exist, even in a multidimensional setting. We derive sufficient conditions for the existence of equilibria, and characterize the spatial locations of two competing parties or candidates when such equilibria exist. The party with the advantage on the valence dimension will generally take a moderate position on the positional issues. We consider the implications of these results for public perceptions of the parties, incumbency advantages, and realigning elections.