Mixed equilibriums in a three-candidate spatial model with candidate valence

We study a spatial model of electoral competition among three office-motivated candidates of unequal valence (one advantaged and two equally disadvantaged candidates) under majority rule assuming that candidates are uncertain about the voters' policy preferences and that the policy space consists of three alternatives (one at each extreme of the linear policy spectrum and one in the center) and we characterize mixed strategy Nash equilibriums of the game. Counterintuitively, we show that (a) when uncertainty about voters' preferences is high, the advantaged candidate might choose in equilibrium a more extremist strategy than the disadvantaged candidates and that (b) when uncertainty about voters' preferences is low, there exist equilibriums in which one of the disadvantaged candidates has a larger probability of election than the disadvantaged candidate of the equivalent two-candidate (one advantaged and one disadvantaged candidate) case.