Two-candidate competition with endogenous valence: a differential game approach

We propose a differential game approach to analyze two--candidate competition in a la Hotelling game with candidates simultaneously choosing locations and investment in valence. We find a Markov perfect equilibrium in which candidates choose divergent locations. Divergence from the median is increasing if the parameter measuring the importance of policy relative to valence is decreasing and if valence depreciates slowly. The results are generalizable to a version of the game with probabilistic voting, that is with a stochastic state equation.