When the Leader Moves First: Political Competition Between Two Incumbents Distinct in Valence

In this work I model political competition between two incumbents, one of whom has an advantage in experience, charisma or other qualities which are not connected to his policy and considered by all voters to be positive (this advantage is termed as valence), under threat of another potential candidate's entry. I consider political competition as a sequential game of two incumbents and one potential entrant where an incumbent with higher valence moves first. I prove that under certain restrictions on a distribution of voters' preferences there exists a unique equilibrium. If the distribution is uniform, then the equilibrium is described explicitly. In the equilibrium the incumbents prevent the potential candidate’s entry. The advantaged candidate's policy is closer to the median voter's most preferred policy, and the second candidate chooses more extreme policy, thus the advantaged incumbent wins the election.