Candidate quality in a Downsian model with a continuous policy space

This paper characterizes a unique mixed strategy Nash equilibrium in a one-dimensional Downsian model of two-candidate elections with a continuous policy space, where candidates are office motivated and one candidate enjoys a non-policy advantage over the other candidate. We show that if votersʼ utility functions are concave and the median voter ideal point is drawn from a unimodal distribution, there is a mixed strategy Nash equilibrium where the advantaged candidate chooses the ideal point of the expected median voter with probability one and the disadvantaged candidate uses a mixed strategy that is symmetric around it. Existence conditions require the variance of the distribution to be small enough relative to the size of the advantage.